- 2 tablespoons warm water (115°F)
- 1/2 teaspoon active dry yeast
- 1 1/3 cups all purpose flour
- 1/3 cup whole wheat flour
- 1/2 cup cool water (65°F to 70°F)
- 1 teaspoon coarse kosher salt
- Cornmeal (for sprinkling)
- 3/4 cup drained roasted red peppers from jar, cut into 1/3-inch strips
- 1/3 cup Kalamata olives, pitted, quartered
- 1 cup Parmesan cheese shavings
- 1 1/2 teaspoons chopped fresh rosemary
- 4 large red onion rings (each 3 1/2 to 4 inches in diameter and 1/2 inch thick)
- 2 cups (lightly packed) arugula
Pour 2 tablespoons warm water into large bowl of stand mixer fitted with dough hook; sprinkle yeast over. Let stand until yeast dissolves, about 15 minutes (mixture will not be foamy). Add both flours, 1/2 cup cool water, and 1 teaspoon coarse salt; mix on medium-low speed 4 minutes. Let rest 5 minutes, then mix on medium speed until dough is smooth, elastic, and slightly sticky, about 3 minutes.
Lightly oil medium bowl. Gather dough into ball and transfer to prepared bowl; turn to coat with oil. Cover bowl with plastic wrap and let rest at room temperature 30 minutes. Chill dough overnight. DO AHEAD Can be made 2 days ahead. Keep chilled.
Transfer bowl to warm draft-free area and let dough rise, covered, until very slightly puffy, at least 2 hours.
Place pizza stone or rimless baking sheet in oven; preheat to 500°F. Sprinkle pizza paddle or another baking sheet generously with cornmeal. Roll out dough on lightly floured surface to 12-inch round; transfer to paddle. Brush dough with oil; scatter peppers, then olives over. Sprinkle with Parmesan and rosemary. Arrange onion rings atop pizza, spacing apart. Slide pizza onto stone or baking sheet in oven; bake until lightly browned but not crisp, about 7 minutes. Remove pizza from oven and gently crack 1 egg into each onion ring. Return pizza to oven and continue to bake until eggs are softly set and crust is golden, about 6 minutes. Sprinkle pizza with salt and pepper. Scatter arugula over.