If using frozen shrimp, thaw them under cool running water. Peel, remove the tails if needed, and pat the shrimp dry with paper towels.
Bring a large pot of salted water to a boil. Cook the angel hair pasta according to the package directions until al dente.
Before draining, reserve about ½ cup of the pasta cooking water.
While the pasta cooks, heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Add the shrimp in a single layer and cook for 2–3 minutes until pink and opaque. Transfer to a clean plate.
Add the remaining olive oil to the skillet along with the grape tomatoes and minced garlic.
Cook until the tomatoes begin to burst and release their juices. If the garlic starts browning too quickly, add a splash of water to the skillet.
Add the drained pasta, basil pesto, and about half of the reserved pasta water to the skillet.
Toss until the pasta is evenly coated, adding more pasta water as needed to create a silky sauce.
Return the shrimp to the skillet and gently toss everything together.
Sprinkle with grated Parmesan cheese and freshly ground black pepper.
Serve your Pesto Shrimp Pasta immediately with extra Parmesan and fresh basil if desired.