Spoon 1/2 the shredded pork onto each tortilla; top each with 2 tablespoons barbeque sauce, 4 Cheddar cheese halves, 1/2 the onion rings, salt, and pepper. Fold opposing edges of each tortilla to overlap the filling. Roll 1 of the opposing edges around the filling into a burrito-shape. Wrap each tightly with aluminum foil and place on a baking sheet.
Bake in the preheated oven until cooked through and cheese is melted, 15 to 20 minutes. Cut each wrap in half to serve.