In a large bowl, beat the eggs with a fork until well blended, then add the grated butter, mixing until well combined. The butter will emulsify into the eggs and keep them fluffy and tender, even when cooked through. Set aside.
Cook Canadian bacon in a lightly greased nonstick skillet or on a flat top until heated through and slightly browned. Set aside and keep warm in a 200° F oven until service.
In a large nonstick pan over, medium high heat melt the rest of the butter. When the butter stops foaming, add the peppers and onion and sauté until the vegetables are soft, about 5 minutes. Season to taste with salt and pepper.
Lower the heat to medium low. Pour the egg and butter mixture over vegetables in pan. Using a heat-proof rubber spatula to scramble the egg mixture until firm throughout with no visible egg liquid remaining, and large curds have formed. Season to taste with salt and pepper.
Place one slice of Canadian bacon on the bottom of each English muffin. Portion cooked egg mixture on top of the bacon, you may find this easier to do with a ring mold, so that you can press the egg mixture down just enough for it to hold well. Top with other half of muffin. Serve hot.