Heat up a little vegetable oil, butter, or bacon grease in a skillet. Saute onion and pepper for 6 to 8 minutes.
Move vegetables over to the side of the skillet and add roast beef. Season with salt and pepper, garlic, Worcestershire, and A1. Heat through and then mix with vegetables.
In another skillet, melt butter. Meanwhile, whisk together eggs and milk until fluffy.
Add eggs to skillet and cook until set, sliding a spatula underneath it every so often to let the uncooked eggs get under the cooked eggs.
Add a little of the meat mixture to one side of the eggs and then add cheese to it.
Flip other half over filling and let the cheese melt.