Flatten each bread slice with a rolling pin until very thin. Trim crusts off bread. Lightly brush both sides of bread slices with melted butter. Cut each bread slice in half diagonally.
With cut sides facing, place 2 bread halves in each of 6 muffin cups, making sure to cover bottom entirely and allowing bread corners to extend above rims. Bake at 375° for 5 minutes or until bread is slightly firm. Remove pan from oven; sprinkle 2 teaspoons shredded cheese into each cup. Top each cup with 2 teaspoons chopped tomato. Crack 1 egg into each cup; sprinkle eggs evenly with salt and pepper. Bake an additional 18 minutes or until whites are set and yolks are still a bit runny or to desired degree of doneness. Remove egg cups from pan; sprinkle evenly with bacon and chives, if desired.