Preheat oven to 400 degrees, with rack in top position.
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, transfer to oven, and bake until liquid is mostly absorbed, 10 to 12 minutes.
Toss shrimp with 1 teaspoon oil and ¼ teaspoon each salt and pepper.
Remove skillet from oven and place shrimp on top of orzo.
Heat broiler.
Broil until shrimp are opaque throughout, 4 minutes.
Sprinkle with basil and serve.
