Preheat oven to 500°F (260°C) and place pizza stone or steel in the oven.
Heat olive oil in a skillet over medium-high heat, add sausage, and cook until browned.
Transfer cooked sausage to a paper towel-lined plate to drain excess fat.
In the same skillet, melt butter and sauté the diced onion until softened and golden brown.
While onions are cooking, prepare the pizza dough on a floured surface.
Spread pizza sauce on the dough, leaving a small border around the edge.
Top with fontina and pecorino cheeses, followed by the sausage and caramelized onions.
Make small wells in the toppings and crack an egg into each well.
Carefully transfer the pizza to the oven and bake for 8-10 minutes.
Remove the pizza from the oven, let cool slightly, and slice to serve.
