Fold four 18x12-inch pieces of heavy foil in half to make four 12x9-inch rectangles. Set aside. Spread roll bottoms and tops evenly with barbecue sauce. Top each roll bottom with a slice of the cheese, cutting to fit if necessary. Top each with ham, cutting thicker sliced ham to fit, if using. Top with bacon, remaining cheese slices and red pepper strips, if you like. Place each roll top, sauced side down, over cheese.
Place each sandwich on a piece of foil. Bring up edges of foil to enclose sandwiches.
For a charcoal grill, arrange medium-hot coals around bottom edge of grill. Test for medium heat above center of grill. Place sandwiches on center of grill rack, not over the coals. Cover and grill for 12 to 15 minutes, or until rolls heated through and cheese is melted, turning once halfway through grilling. (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Grill as above.) Serve warm. If you like, serve with pickles. Makes 4 sandwiches.
Place individually wrapped sandwiches in an insulated cooler with ice packs. At tailgating site, grill sandwiches as directed above in step 3.
Assemble sandwiches as directed above through step 2. Chill wrapped sandwiches up to 8 hours.