Preheat oven to 400ºF. Spread the pizza crust on a baking sheet and bake for 5 minutes.

In a large skillet, cook the chopped bacon until crisp and remove to a plate. Drain all but 1 tablespoon of the bacon drippings from the skillet. Add the eggs and milk to a bowl and whisk until well combined. Pour the eggs into the skillet with bacon drippings and scramble until just set, about 2-3 minutes.

Mix the mayonnaise and Dijon mustard in a small bowl and spread a thin layer over the pizza crust as a "sauce". Add the scrambled eggs over the sauce, then top with the cheddar cheese and bacon. Bake the pizza for another 5-7 minutes until the crust is golden and the cheese is melted. Sprinkle with chopped green onions and cut into slices to serve.