Combine 3 tablespoons vinegar and garlic in a small bowl; brush over both sides of eggplant slices. Sprinkle both sides of eggplant with pepper and salt. Place eggplant on grill rack coated with cooking spray; grill 2 minutes per side or until tender. Remove from grill; set aside.
Place 1 crust on grill rack coated with cooking spray; grill 3 minutes or until puffy and golden. Turn crust, grill-mark side up; brush with 1 teaspoon oil. Arrange half of eggplant slices over crust, overlapping slightly. Top with half of tomato, cheese, and oregano. Cover and grill 3 to 4 minutes or until thoroughly heated; remove from heat. Combine spinach and 2 tablespoons vinegar in a small bowl. Top pizza with half of spinach mixture. Repeat with remaining crust and toppings.