Combine the mayo and 2 tablespoons of the barbecue sauce in a small bowl. Whisk to combine; Set aside.
Preheat your grill for cooking and grease the grates.
Mix the remaining 4 tablespoons barbecue sauce and ground beef in a large bowl. Divide into 2 large halves, then divide each half into 4. Press each into a thin wide patty, about 4 inches wide. Using your thumb, or the back of a spoon, create an indent in 4 of the patties. Fill each of the indents with the cheddar cheese. Top the patties with the remaining 4 patties and pinch the edges to seal. Season the outside of the patties with salt and pepper.
On your preheated grill, grill the patties for 10 to 12 minutes, flipping once halfway through. Carefully remove the burgers from the grill and allow to rest. Meanwhile, toast your hamburger buns.
Prepare the burgers for serving by arranging lettuce on toasted buns, top with a cooked burger, spoon a bit of the barbecue mayo sauce mixture over each patty, sliced onion, and the kettle chips. Lastly, top with the buns and serve.