Heat the oven to 400°F and line a rimmed sheet pan with parchment. Sauté bell pepper and onion in oil over medium heat for 6 minutes, then cool for 5 minutes.
Stir cracker crumbs, milk and egg together and let stand for 5 minutes. Fold in beef, cheddar, cooled vegetables, salt and pepper.
Divide into 6 equal portions and shape each into a 4-by-2-inch oval loaf about 1 1/2 inches thick, spaced apart on the pan.
Bake for 15 minutes. Stir ketchup, mustard and brown sugar together and brush over the loaves.
Bake for 10 to 14 minutes more until the centers reach 160°F. Rest for 5 minutes.
Serve one mini loaf per portion, keeping any escaped melted cheese with its loaf.