- For cheese sauce, in a saucepan, melt butter. Stir in flour until smooth; gradually add the milk. Bring to a boil; cook and stir for 2 minutes or until thickened. Reduce heat to medium-low.
- Add the cheese, mustard, salt and pepper, stirring until cheese is melted. Cover and keep warm.
- In a skillet with high sides, bring 2-3 inches of water and vinegar to a boil. Reduce heat; simmer gently. For each egg, break the cold eggs into a custard cup or saucer, hold the dish close to the water surface; slip the egg into the water. Cook 4 eggs at a time, uncovered, for 3-5 minutes or until the whites are completely set and the yolks begin to thicken.
- With a slotted spoon, remove each egg. Repeat with remaining eggs. To assemble, top each slice of toasted bread with a slice of bacon, one egg and cheese sauce.