Preheat oven to 350ºF. Grease a 9x13-inch baking dish with nonstick cooking spray.
In a large skillet over medium heat, cook the ground beef until it's no longer pink, stirring and breaking it up as it cooks, about 7 minutes. Drain the excess fat from the skillet.
Add the diced green pepper to the skillet and continue to cook for 3 minutes.
Stir in the can of sloppy joe sauce. Continue to cook over medium heat for 3 minutes, until everything is well combined and heated through.
Slice the rolls in half, horizontally. Place the bottom halves into the prepared baking dish.
Evenly spoon the sloppy joe mixture onto the bottom halves of the slider rolls in the baking dish.
Layer the slices of cheddar cheese on top of the meat mixture.
Place the top halves of the slider rolls onto the cheese.
Whisk together the melted butter, garlic powder, Dijon mustard, Worcestershire sauce, and brown sugar in a small bowl.
Brush the glaze evenly over the tops of the slider rolls, making sure to cover all the edges and crevices.
Cover the baking dish with aluminum foil and bake in preheated oven for 15 minutes.
After 15 minutes, remove the foil and bake for another 5 minutes or until the rolls are golden brown.
Remove from the oven and let cool slightly before serving. Cut along the lines of the rolls to create individual sliders.