Preheat the oven to 260°C (500°F) 30 minutes before baking the pizza.
Generously dust the surface of a pizza peel or large inverted sheet pan with flour; place the pizza crust on it.
Sprinkle the crust with the cheeses and bacon. Top with the tomato and mushroom slices. Crack the 3 eggs over the top. Season with salt and pepper.
Bake the pizza using the top and bottom heat + fan function for 5 minutes, then rotate and cook for 3 to 5 minutes more. Check the pizza. The crust should be golden and the egg whites cooked. Remove from the oven and cool for a few minutes.
Top with the arugula and parsley. Serve immediately while hot.