1. In a large broilerproof skillet, heat 5 teaspoons oil over medium. Add garlic and cook until just beginning to brown, 1 minute. Increase heat to high and add tomatoes; season with salt and pepper and cook, stirring occasionally, until softened, 6 minutes. Add orzo and broth and bring to a simmer. Cover and simmer until liquid is mostly absorbed, 10 to 12 minutes. Meanwhile, preheat broiler with oven rack in top position.
2. Toss shrimp with 1 teaspoon oil and 1/4 teaspoon each salt and pepper. Remove skillet from heat and place shrimp on top of orzo. Heat broiler. Broil until shrimp are opaque throughout, 4 minutes. Sprinkle with basil and serve.