Melt butter in a med. Size sauce pan.
Add flour and stir.
Gradually add milk until you have a nice consistency for gravy. Add a little more milk if it is too thick.
Add grated cheese and mix until it is well blended. Add mustard. You may want more mustard if you like a stronger taste. Set aside.
Toast your muffins, and poach your eggs. If you don’t have an egg poacher pan you can poach your eggs in water or in milk. If you poach them in milk then use the leftover milk to make the gravy with.
Fry or microwave Canadian style bacon until it is warm.
Layer as follows: English muffin, Canadian bacon, poached egg and top with sauce.