Pre-heat a 4-quart non-stick sauté pan over medium-high heat. Add the ground beef and break it up with a wooden spoon as it browns. Add the onions and continue to cook until there is no more pink left in the meat. Drain the grease from the pan and then return it to the stovetop.

Add the green peppers, diced tomatoes, tomato paste, brown sugar, apple cider vinegar, Worcestershire sauce, mustard, salt and pepper. Bring the mixture to a boil and then reduce the heat and simmer for 20 minutes.

Remove the pan from the heat and sprinkle 2 cups of Monterey Jack cheese evenly over the beef mixture.

Split the slider rolls in half and arrange them in the pan on top of the meat and cheese with the cut side facing up. Brush the melted butter onto the cut surface of the rolls. Sprinkle the remaining Monterey Jack cheese on top and transfer the pan to the oven.

Bake at 350ºF for 25 minutes, or until the rolls are toasted brown and the cheese has melted.