Place dough in a microwave-safe bowl; microwave at MEDIUM (50% power) for 45 seconds. Let stand 5 minutes. Roll dough into a 14-inch circle. Place on a pizza pan; pierce with a fork. Combine 1 1/2 tablespoons oil and garlic; brush over dough. Bake at 450° for 14 minutes.
Heat a large nonstick skillet over medium heat. Add remaining 1 1/2 teaspoons oil; swirl to coat. Crack eggs into pan; cook 4 minutes or until whites are set. Sprinkle with salt.
Combine mâche, onion, and vinaigrette. Arrange on crust; top with eggs, cheese, and pepper.