1. Preheat oven to 450°.
2. Unroll pizza dough on a baking sheet lightly coated with cooking spray; place in preheating oven. Bake as oven heats for 7 minutes.
3. Combine the ricotta and 1/4 cup Romano. Remove pan from oven. Quickly spread cheese mixture over dough, leaving a 1/2-inch border around the edges. Return pan to oven, and bake for 5 minutes.
4. While pizza bakes, add water to a large skillet, filling two-thirds full; bring to a boil. Reduce heat; simmer. Add vinegar. Break each egg into a custard cup, and pour gently into pan. Cook 3 minutes or until desired degree of doneness. Carefully remove eggs from pan using a slotted spoon.
5. Combine arugula, remaining 1/4 cup Romano cheese, and the next 4 ingredients (through salt) in a large bowl; toss well. Top pizza with arugula mixture and eggs; sprinkle with pepper. Cut into 6 pieces.