In a large skillet, heat over medium-high heat, and add the ground beef. Sauté until the meat is deeply browned, approximately 5-7 minutes.

In the same skillet, add butter and allow it to melt over medium heat. Toss in the diced onions and bell peppers, letting them sauté for 1-2 minutes.

Once the vegetables are softened, drain any excess grease from the skillet, and return the browned ground beef to the pan.

Let the mixture simmer on medium heat for about 3-5 minutes until it thickens.

Once thickened to your liking, remove from heat and stir in the cheddar or mozzarella cheese.

Heat another skillet over medium heat and add a bit of butter. Lightly toast the brioche buns for 2-3 minutes.

Once the buns are toasted, generously spoon the beef mixture onto the warm brioche buns.