1 cup (packed) fresh spinach (about 2 ounces)

1 cup (packed) arugula leaves (about 2 ounces) plus additional (for garnish)

1/2 cup plus 2 tablespoons extra-virgin olive oil plus additional (for brushing)

4 garlic cloves, coarsely chopped

1 cup (or more) warm water (110°F to 115°F), divided

1 tablespoon honey

2 1/4-ounce packets active dry yeast

3 cups all purpose flour

1/4 teaspoon coarse kosher salt

Cornmeal (for sprinkling)

8 ounces fingerling potatoes, cooked, cooled, cut crosswise into 1/3-inch slices

8 ounces asparagus; thin stalks cut into 1/2-inch pieces, thick stalks cut into 1/4- to 1/3-inch pieces

2 large ears of corn, husked, kernels cut from cobs

2/3 cup fresh peas or frozen peas, thawed

3/4 cup ricotta cheese (not drained)

8 large eggs

Parmesan cheese shavings

 

Place spinach in microwave-safe bowl. Sprinkle with water. Microwave until wilted, about 20 seconds. Drain, pressing on spinach to release liquid. Place spinach, 1 cup arugula, 1/2 cup oil, and garlic in blender. Blend until coarse puree forms. Transfer pesto to small bowl. Season to taste with salt and pepper. DO AHEAD Can be made 1 day ahead. Cover and chill. Stir 1/4 cup warm water and honey in small bowl. Stir in yeast. Let stand until foamy, about 10 minutes. Place flour and coarse salt in stand mixer fitted with dough hook attachment. Add 3/4 cup warm water and yeast mixture. Mix on medium speed until dough comes together and pulls away from sides of bowl, adding more water by tablespoonfuls if too dry, about 2 to 3 minutes. Brush large bowl with oil. Form dough into ball. Place in bowl; turn to coat. Cover with plastic; place in warm draft-free area until doubled in volume, about 1 hour. Place pizza stone or baking sheet in oven (if using rimmed baking sheet, invert sheet, rim side down). Preheat oven to 500°F. Knead dough in bowl. Cover and let rise again until doubled in volume, about 45 minutes. Divide dough into 4 equal portions. Form each portion into ball. Place on floured work surface; cover with plastic wrap and let rest 10 minutes. Sprinkle rimless baking sheet with cornmeal. Working with 1 ball at a time, roll out dough on floured surface to 12×7-inch oval. Transfer to sheet. Spread 2 tablespoons pesto over dough, leaving 1/2-inch plain border. Sprinkle 1/4 of potatoes, 1/4 of asparagus, 1/4 of corn, and 1/4 of peas over pesto. Spoon three 1-tablespoon dollops ricotta over vegetables. Slide pizza onto stone; bake until crust is golden brown on bottom and around edges, 10 to 12 minutes. Meanwhile, brush nonstick skillet with oil; heat over medium heat. Crack 2 eggs into skillet; cook just until whites are set but yolks are still runny, about 3 minutes. Transfer pizza to work surface. Place 2 fried eggs atop pizza. Scatter shaved Parmesan and arugula leaves over. Cut pizza into wedges and serve. Repeat with remaining dough, pesto, potatoes, asparagus, corn, peas, ricotta, and eggs.