In a skillet, saucepan, or omelet pan with high sides, bring 2-3 in. water to a boil; reduce heat, simmer gently.
Break cold eggs, one at a time, into a custard cup or saucer.
Holding the dish close to the surface of the water, slip eggs, 1 at a time, into the water.
Cook, uncovered, until whites are completely set and yolks begin to thicken (about 3 minutes).
Spread cream cheese over muffin halves
Top with cheese slices.
In a small skillet, cook Canadian bacon until heated through.
Place over cheese.
Using a slotted spoon place eggs over bacon.