Preheat oven to 425°F Place pizza crust on large baking sheet.
Mix olive oil and minced garlic in small bowl. Using pastry brush, brush 2 tablespoons garlic oil evenly over crust. Top with spinach leaves, then sprinkle with sliced mushrooms, roasted red peppers, red onion slices, fresh basil, and crumbled goat cheese.
Drizzle pizza evenly with remaining garlic oil.
Bake pizza until crust is crisp and cheese begins to brown, about 18 minutes. Transfer pizza to board. Cut into wedges and serve warm.