Mix eggs and milk together is a bowl. Add in chives and cheese and blend.
In a large, non-stick skillet, melt butter over a medium heat. Add egg mixture and let set. Keep lifting up the sides of the egg around the pan to let the non-cooked eggs get contact with the skillet. Once fully cooked, pull pan off heating element and let set for a minute.
While the eggs are cooking, put English muffins in the toaster to brown.
Using a wide-rimmed glass, "cut out" eggs in the pan to get a round-"English muffin-sized" egg. Place cutouts on the bottom of the English Muffins.
In a small skillet, add half a tablespoon of butter and brown Canadian bacon on each side. Place the Canadian bacon on top of the egg rounds and top with the other half of the English muffin.