Using a 4.5-inch round pastry cutter, cut 12 rounds from the dough. Place 6 rounds on a parchment lined baking sheet.
Season beef with salt and pepper, and form into 6 evenly sized mini patties that are about a half inch smaller in diameter than the biscuit rounds. Place each patty on a biscuit round.
Evenly distribute onions, cheese, and bbq sauce on top of the patties. Using a pastry brush, dab the whisked egg onto the edges of the biscuit dough surrounding the beef patty.
Top each patty with a second round of dough pressing down as needed, and crimp the edges with a fork.
Brush the cheeseburger stuffed biscuits with the egg wash, poke the tops of them with a fork (to create a little ventilation) and bake until the biscuits are fully cooked, about 20 minutes. Enjoy with your favorite burger sides, like sweet potato fries!