In a large skillet set over medium heat, melt the butter. Add the onions and bell peppers. Cook until softened, 6 to 7 minutes, stirring frequently.

Add the ground beef and use a wooden spoon to break it up into small pieces as it cooks. Cook until the meat is browned, 5 to 6 minutes.

Stir in the stock, ketchup, Worcestershire sauce, garlic powder, salt, and black pepper. Turn the heat down to low and simmer for 4 to 5 minutes until the mixture thickens. Stir in the cut cheese right before serving.

Toast the brioche buns. Lay the remaining slices of provolone cheese on each brioche bun half. Top with spoonfuls of the sloppy joe mixture and the top bun. Serve warm.