Thinly slice the onion. Cook the onions in a nonstick skillet over medium heat for 5-7 minutes, stirring occasionally, until soft and lightly caramelized.
Divide 1 lb. of lean ground beef into 4 equal portions, then form into thin patties. Season both sides with salt, pepper, and garlic powder.
Lay the 4 tortillas flat. Cut a slit halfway up the center of each tortilla to create 4 sections.
Divide the ingredients evenly among the wraps. Each wrap will get one hamburger patty, grilled onions, 1 tablespoon of BBQ sauce, and 2 tablespoons of shredded cheddar cheese.
Fold each quarter over the next to form a layered wrap. Place the filded wraps back into the skillet (or a panini press) and cook 2-3 minutes per side, until golden and the cheese is melted. Serve warm and enjoy!