1. Remove dough from refrigerator. Let stand at room temperature, covered, for 20 minutes.
2. Place a pizza stone or heavy baking sheet in oven. Preheat oven to 500° (keep pizza stone or baking sheet in oven as it preheats).
3. Heat a small skillet over medium heat. Add oil to pan; swirl to coat. Add garlic; cook 2 minutes or until garlic is lightly browned. Remove garlic with a slotted spoon. Finely chop garlic. Reserve oil.
4. Place chopped garlic, ricotta, mayonnaise, thyme, pepper, and Parmigiano-Reggiano cheese in a medium bowl. Beat with a mixer at medium-high speed until almost smooth (about 2 minutes).
5. Roll dough into a 14-inch circle on a lightly floured surface; pierce entire surface of dough liberally with a fork. Carefully remove pizza stone from oven. Arrange dough on pizza stone. Bake at 500° for 5 minutes. Spread ricotta mixture over crust, leaving a 1/2-inch border. Arrange mozzarella over ricotta mixture. Bake at 500° for 10 minutes or until crust and cheese are browned.
6. Combine reserved oil, juice, and vinegar in a medium bowl. Add arugula; toss to coat. Top pizza with arugula mixture. Cut pizza into 4 large pieces.