Brisket, Ribs, Pulled Pork, Burgers, Burritos, Quesadillas Established in 2020. Long Island Barbecue Restaurant Big Belly Que is a full service barbecue restaurant, located in Smithtown NY. Big Belly Que started with their catering company Big Belly BBQ which was started by three friends who have a real passion for food. The co-founders Matt and Chris and Patrick have been working in the food industry collectively for over two decades. With their knowledge of cooking and passion for barbecue, Big Belly Que will blow your mind with their BBQ Mexican fusion. Big Belly Que offers a wide variety of option including Vegan BBQ Options! Big Belly Que provides the level of detail needed to make sure that every dish that you order from them will be just as delicious as the last. Big Belly Que will only leave memories of great food and possibly the meat sweats.