How to Make It
Heat oven to 425° F. Shape the dough into 4 rounds. Brush both sides with 1 tablespoon of the oil and place on 2 baking sheets. Dividing evenly, sprinkle with the Asiago and bake until golden, 12 to 15 minutes.
Meanwhile, heat the remaining tablespoon of oil in a large nonstick skillet over medium heat. Crack the eggs into the skillet and cook, covered, 2 to 3 minutes for slightly runny.
Dividing evenly, top the baked dough with the chicken, arugula, pesto, fried eggs, and ¼ teaspoon each salt and pepper.