Roll out the pizza dough on a lightly floured surface until you reach your desired size. Be careful not to roll too thin. Place on a large baking sheet or pizza stone.
Spread the fig jam over the surface of the dough. Lay the slices of mozzarella on top and sprinkle the cheese lightly with salt and pepper. Top with prosciutto, carefully crack 1 egg over the top of the pizza (if using) and season the egg with salt and pepper.
Bake the pizza until the crust is golden, the cheese is bubbly and the egg whites are fully cooked, 15-20 minutes.
Pull pizza from oven and let cool for 10 minutes. Toss arugula with olive oil and pile on top.