Mix together the onion, green pepper, milk, sugar, and one cup of the cracker crumbs. Add the cooked carrots, and mash all the ingredients together. Top with salt and pepper and the remaining one cup of cracker crumbs, and dot with the room-temperature butter. Bake in a 325-F degree oven for 35 to 40 minutes, or until the top is brown. Place sausage in bottom of lightly greased 9x13 casserole.
Layer croutons over sausage.
Cover sausage and croutons with grated cheese. Mix eggs and milk in a bowl. Pour egg and milk mixture over sausage, croutons and cheese. Sprinkle dry mustard on top. Salt and pepper to taste.