Place a pizza stone or large baking sheet in oven; preheat to 450°F (leave stone in oven as it preheats).
Let dough stand at room temperature for 30 minutes. Divide dough into 4 pieces.
On a lightly floured surface, press 1 piece of dough into a 7-inch circle. Pierce liberally with a fork.
Arrange 2 dough circles on hot pizza stone. Bake in preheated oven for 3 minutes. Remove from oven, and flip so cooked side is up. Set aside. Repeat with remaining 2 dough circles.
Stir together ricotta cheese and zest in a medium bowl. Divide ricotta mixture evenly among cooked sides of dough circles; sprinkle evenly with ⅛ teaspoon salt and ⅛ teaspoon pepper. Top each dough circle with 1 egg and 1 tablespoon Parmesan.
Working in 2 batches, return topped dough circles to pizza stone. Bake at 450°F until egg whites are set and yolks are still a little runny, about 5 to 8 minutes.
Whisk together oil, juice, remaining ⅛ teaspoon salt, and remaining ⅛ teaspoon pepper in a large bowl. Stir in arugula. Top each pizza with arugula mixture.
