Description Between Rounds Franchise Corp. operates a chain of a half dozen bagel shops under the banner Between Rounds Bakery Sandwich Cafe. Found in Connecticut and Massachusetts, the quick-casual eateries offer a menu of bagels, breakfast sandwiches and baked goods, as well as soups, salads, and lunch sandwiches. In addition to dining, the restaurants offer catering services. Jerry and Laurie Puiia opened their first shop under the Bagel Stop name in 1990.