Preheat oven to 425°F. Roll out crust to fit a jelly-roll pan. (If you don't have one, make it 15x10-inches on a cookie sheet.) Brush crust with 1 tablespoon olive oil and sprinkle with garlic. Top with shrimp and tomatoes; bake for 12 minutes.
Remove pizza from the oven. Sprinkle it with basil and cheese. Drizzle with the remaining oil. Return to the oven just until cheese is melted, about 7 minutes. Season with pepper and allow the pizza to cool slightly before serving. Cut into 12 rectangular slices.