If you can, get a piece of slab bacon. If none is available, look for the thickest cut sliced bacon. Chop them up.
In a large wok, heat 1 ½ tablespoons of the butter over medium to medium-low heat. Add the bacon and fry for 5 to 6 minutes, frequently stirring, until the bacon pieces are lightly browned.
Add the shiitake mushrooms and stir fry for 2 minutes until slightly browned.
Add the rice and pepper, and combine well, getting the rice evenly coated with the butter or bacon fat in the frying pan. Heat the rice for 5 minutes, stirring occasionally.
While the rice is frying, heat the remaining ½ tablespoon of butter over medium-low heat in a small frying pan. Add the beaten eggs and cook, frequently stirring, until you have soft scrambled eggs. Turn the heat up to medium and fry (without further stirring or scrambling) for ½ minute until the outside is slightly golden.
Use a wooden spatula to break the egg into small pieces.