Build the pizza: Preheat the oven according to pizza package directions. Pile a few pieces of ham into a stack and then roll it up and cut into really thin strips. Continue with the rest of the ham.
Place the pizza onto a pizza pan. Pile the ham onto the pizza in four nests, each with a little well in the center. Crack an egg into the well of each ham nest. Sprinkle the entire pizza with the Gruyère cheese and a pinch of oregano. Place the pizza into the oven and cook according to package directions or until the white of the eggs are cooked with the yolks are a little runny.