Bring a large pot of lightly salted water to a boil. Cook angel hair pasta in boiling water, stirring occasionally, until tender yet firm to the bite, 4 to 5 minutes. Drain; keep warm.

Melt 2 tablespoons butter in a large skillet over medium heat. Cook shrimp in hot butter, stirring occasionally, until the meat is opaque and bright pink on the outside, 3 to 4 minutes. Use a slotted spoon to transfer shrimp to a warm plate.

Cook and stir garlic in the same skillet over medium heat until fragrant, about 1 minute. Add tomato, remaining 6 tablespoons butter, basil, and extra-virgin olive oil. Stir in cooked shrimp.

Serve over warm pasta and garnish with additional basil.