Chef John's Sausage and Egg Pizza

Ingredients (11)

• + 6 ounces hot Italian sausage, sliced add to pantry
• + 12 ounces unbaked pizza dough, at room temperature add to pantry
• + 2 tablespoons cornmeal, or as needed add to pantry
• + ¾ cup pizza sauce add to pantry
• ✓ 1 pinch red pepper flakes, or to taste
• + 6 ounces shredded Fontina cheese, divided add to pantry
• + 4 eggs add to pantry
• + freshly ground black pepper to taste add to pantry
• ✓ ⅓ cup freshly shredded Parmigiano-Reggiano cheese, divided
• + 1 cup baby arugula leaves, washed and dried add to pantry
• ✓ 1 tablespoon olive oil