And the winner of the fast-food wars in the second quarter: McDonald's (MCD - Get Report) , thanks to a flood of offers for $1 hot coffee and $2 iced frappes.

Dunkin' Brands (DNKN - Get Report) reported Thursday that same-store sales at its U.S. Dunkin' Donuts chain rose 0.8%, falling short of Wall Street's estimate for a 1.3% increase. Net sales came in at $218.5 million compared to analyst forecasts for $220.7 million. Dunkin' did manage to beat on earnings, notching 64 cents a share vs. the 61 cents a share expected.

The coffee and donut chain reaffirmed its Dunkin' U.S. same-store sales estimate for the year of a low-single digit increase. Earnings are still seen in the range of $2.40 to $2.43 a share.

It was a slightly different story at McDonald's on Tuesday. 

In the U.S., McDonald's same-restaurant sales increased 3.9%, versus the 3.1% expectation on Wall Street. Globally, they rose 6.6%.

TheStreet spoke with Dunkin' Brands CEO CEO Nigel Travis on Wednesday about what the future of Dunkin' holds. What follows is a condensed and edited version of our conversation.

Q: It sounds like you're developing a new restaurant layout. Anything you can peal back on that, what that might look like?

Travis: Dave [Hoffmann, president of Dunkin' Donuts U.S. and Canada] has done a lot of great things for this business. I think he's really helped us realize the value of drive-thrus, so that's one point. Secondly, I think we were already a digital leader. We didn't talk a lot about it on the earnings call today, but in our view, we're an established leader in digital, and we'll continue to be, so that's the second point. The third point is our research last year that we did, most people told us we have to be focused on beverages and on the go. That's what our consumers want, and there's a lot more stuff that goes behind that, but that's essentially the summary of what they want.

As a result of that, our restaurants have to change, and I suppose I'd add as a fourth point, restaurants need to change regularly just to stay up to date. I sometimes go into other restaurants, and it's usually because they look good, so you need to keep your restaurants up to date. When I got here, we weren't perhaps as disciplined as we should have been about making people do their remodels.

We're totally disciplined now, but from time to time, you need to move to a new store design. That new store design will be very much focused on beverages, will be very much focused on convenience, and as a result of that, the drive thru will be paramount. The technology like how we incorporate on the go will be a part of that; new contemporary design features, which obviously we're still working through, will be part of it and our intention is to show it to analysts and journalists as soon as possible.

Q: Will it have a Baskin-Robbins inside of it?

Travis: The ones that we develop may well have Baskin, because it depends on where it is. Most of our franchisees in Chicago, Baltimore or Detroit may well have a Baskin-Robbins. Some out West may have a Baskin-Robbins. Some in New York may have a Baskin-Robbins. We obviously need to incorporate that, and one of the things we're doing at the same time that we didn't talk about in the conference call is Jason [Maceda, senior vice president of Baskin-Robbins U.S.] is thinking about the next store design for Baskin-Robbins. If we open new stores in the next couple of years, they will hopefully have the new design for Baskin and the new design for Dunkin'.

Q: You're expanding your menu simplification to total 1,000 locations. How are people responding to that? I'm sure there are people who are obsessed with certain things each morning.

Travis: You're obviously right. I had someone talking to me the other day, and they actually admitted to me that they go into Dunkin' every day, and they order the same thing every day. They never look at the menu board; they just go into Dunkin' and order the same thing. That's true, but a lot of customers have said that our menu is fairly complicated. We did a lot of research on this. They find it a little bit, as I said, complex and confusing, so we listen to what the consumer does because the customer is at the center of everything we do. We took that as one data point.

Another data point was the franchisees felt our store was complicated, and as I've said, I think to you previously, "Wow, this is more complicated to operate than a McDonald's," which was kind of an amazing statement.

So we heard that from our franchisees, and that's what got us started on thinking about menu simplification, and the feedback from customers, from franchisees, from employees has been universally outstanding, so that's why we're taking it to the next stage. I want to say a very important thing: We're still in test mode. It doesn't mean we're going to roll it out, and as I said on the call, the test may vary by region.

Dunkin' Brands CEO Nigel Travis.
Dunkin' Brands CEO Nigel Travis.

Q: Earlier in the week on the McDonald's earnings call, CEO Steve Easterbrook mentioned that their comeback is bringing "pain" to sandwich players. Have you seen any impact at Dunkin' as McDonald's has come back?

Travis: Firstly, congratulations to McDonald's on their same-store sales. Clearly, they're a sandwich player, and I think the top two sandwich players in the morning are us and McDonald's. What I'd say, though, is our breakfast sandwiches had a spectacular quarter. As I also said, the afternoon is an area we need to focus on, but, hey, if you asked me what is more important, all the research tell us people are more focused on coming to Dunkin' in the morning. That's the growth area, so we were delighted with our sales and our traffic improvement. Our traffic improvement in the morning, we will continue to work on that, and we will continue to dissect the afternoon.

By the way, just to put everything into context, we have very steady comps, and if you look over a four-year stack, our comps were nearly 6%. I'd ask you to compare with McDonald's four-year stack.

Q: Also, on delivery, are you expanding that to more markets?

Travis: We launched delivery in mid-2016. We're expanding it; we're door dashing out of the Miami market. We now have it in about 750 Dunkin' stores. I believe that the food delivery trend is just starting, I think. I've talked to people overseas, and delivery is bigger than it is in the U.S. One thing we talked about in the call is integrating catering. Down the road, we've got plans I'm not going to reveal today to make delivery more integrated. Baskin-Robbins has just launched delivery, and that's going into more than 600 stores in 22 cities.

Then, internationally, we're absolutely delighted with what's happened with delivery. Firstly, in the Middle East, it's up significantly. I think it's up like 33%, and we feel delivery is clearly the mode of the future. It's a global trend. We're testing Dunkin' delivery in 11 markets, which right now are Bahrain, Korea, Thailand, China, UAE, Netherlands, Peru, Philippines, Vietnam and the U.K. Baskin is already in 11 markets altogether, and we have fantastic results coming out of Saudi Arabia and Kuwait.

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