What’s KEY here is the order of things. The bacon needs to be ready for the muffin, the muffin needs to be ready for the burger, and the burger needs to be ready for the egg. So the order of events is:
1. Cook your bacon until it is done just the way you like it. Ordinarily I like cooking bacon in the oven, but in this case we want to do it in the pan because we are going to cook the burger in the bacon drippings. Yes we are.
2. Toast the muffin until it is just starting to brown on the edges (if it’s too toasted, it will break part while you are eating your burger) and then spread it with some nice soft butter. Put both halves on the plate and put a piece or two of bacon on the bottom half.
3. Cook up that burger. 3-4 minutes per side for medium rare, and do not touch it except to flip it please. When it’s done, pop it on top of the bacon.
4. In that same pan, cook an egg over easy. A minute or two on the first side, just until the whites are set, flip very carefully, count to 10 and slide the spatula under the egg and put it on top of the burger.
5. Place the top of the muffin on the egg. Pick the whole thing up. Take a bite. Have napkins at the ready. Be very happy.