How to Make It
Set a pizza stone on the bottom of the oven and preheat the oven to 500°.
On a lightly floured work surface, stretch and roll the pizza dough into a 14—inch round. Transfer the dough to a floured pizza peel, shaking it to make sure it doesn't stick. Brush the edge of the dough with 1 tablespoon of the olive oil and sprinkle on the rosemary. Arrange the pancetta slices on the dough, overlapping them slightly. Bake the pizza for 8 minutes, until the dough is golden and crisp.
Meanwhile, bring a deep medium skillet of water to a simmer. Crack the eggs into individual cups and slide them to the water. Poach the eggs in the simmering water for 4 minutes, until the whites are set but the yolks are still runny. In a large bowl, mix the remaining 2 tablespoons of oil with the lemon juice and the Parmigiano—Reggiano. Season with salt and pepper and toss with the arugula.
Mound the arugula salad on top of the pizza. Using a slotted spoon, transfer the eggs to the pizza. Cut the pizza into 4 wedges and serve immediately.