Add water to a medium skillet to depth of 2 inches; bring to a boil. (While water comes to a boil, prepare Cheddar Cheese Sauce.) Reduce heat to low. Break eggs, one at a time, into a saucer; slip eggs, one at a time, into simmering water, holding saucer as close as possible to surface of water. Simmer 6 to 7 minutes or until internal temperature of egg reaches 160 (yolk will be solid).
While eggs simmer, place muffin halves and tomato slices on a baking sheet. Broil 4 inches from heat (with electric oven door partially opened) 4 minutes or until muffins are toasted and tomato slices are warm.
Spread muffins with mustard; top each with a tomato slice.
Remove eggs from water with a slotted spoon, and place over tomato slices; top with Cheddar Cheese Sauce.
