Place a pizza stone (or baking sheet) on the middle rack in the oven. Heat oven to 500 degrees. For the pesto, place arugula, oil, pistachios, garlic and red pepper flakes in a food processor. Pulse until smooth. Season with the salt and pepper to taste.
Roll or stretch dough into disks, about 10 inches in diameter, on a lightly floured surface. Generously dust a pizza peel or the underside of a cookie sheet with cornmeal or semolina. Lay 1 dough disk on top. Spread half the pesto over the dough; sprinkle with half the cheeses. Crack 1 egg in the center.
Gently slide pizza onto pizza stone. Bake until cheese is melted and egg white is cooked through, 8 to 12 minutes; edges of crust should be golden brown. Remove from oven; cool slightly. Top with fresh arugula. Repeat for second pizza.
Nutrition information per each of 6 servings:
Calories630Fat43 gSodium768 mg