Heat a large skillet over medium-high heat. Add the lean ground beef and diced onion along with salt, black pepper, garlic powder, and onion powder.
Stir in the Worcestershire sauce, tomato sauce, ketchup, yellow mustard, and BBQ sauce. Lower the heat and let the mixture simmer for about 10 minutes until it thickens slightly.
Spoon a generous layer of the sloppy joe meat mixture onto each roll, then sprinkle evenly with shredded cheddar cheese. Place the top halves back on the sliders.