Place baking stone inside oven and heat to 500 degrees for one hour.*
Remove the woody ends of the asparagus. Remove the tips and set aside. Thinly slice asparagus on a sharp diagonal and place in a large bowl with the tips.
Thinly slice onion crosswise and place in bowl.
Drizzle olive oil over the asparagus and season with salt and pepper. Set aside.
Divide dough in half. Place first half on a floured work surface and roll or stretch into a 10 to 11-inch circle.
Place dough circle on a sheet of parchment paper.
Sprinkle with half of the fontina cheese and top with half of the asparagus mixture.
Slide pizza onto preheated baking stone and cook until golden brown, 10 to 12 minutes, turning after 5 minutes.
Remove pizza from oven and crack two eggs over the top. Return to oven and cook until egg whites are set, but the yolks are still runny, 2 to 4 minutes.
Remove pizza and place on a cutting board. Sprinkle with half of the Parmesan cheese and chopped chives. Slice and serve.
Repeat the process for the second pizza.**
*if you do not have a baking stone, substitute (2) baking sheets.If not using parchment paper, rub baking sheets with oil. Do not rub oil on a baking stone.**I have never baked two pizzas at one time, I do not trust my oven. Feel free to give it a try if you like.Make sure your eggs are room temperature or your crust will over cook while the cold eggs cook.