Sauté ham, onion, and garlic in 1 tablespoon butter in a large skillet for 3 minutes. Add tomato, green pepper, salt, and pepper; cook over medium heat for 15 minutes or until liquid is absorbed.
Remove crust from each slice of bread, and cut each slice into 1- x 3-inch strips. Brush bread strips with melted butter. Place on ungreased baking sheet, and lightly toast.
Spread ham mixture over bread strips; sprinkle with cheese. Bake at 350° for 5 minutes. Serve hot.