Toss shrimp with olive oil, lemon juice, garlic, salt, pepper, and paprika in a bowl and let marinate for 15–20 minutes.
Bring a large pot of salted water to a boil and cook pasta according to package directions until al dente.
Reserve ½ cup pasta water, then drain the pasta.
Return pasta to the pot and toss with pesto, olive oil, Parmesan cheese, and black pepper.
Add reserved pasta water as needed to create a silky sauce and fold in halved cherry tomatoes if using.
Preheat grill or grill pan to medium-high heat and grill shrimp for 2–3 minutes per side until pink, opaque, and lightly charred.
Twirl pesto pasta into a mound using tongs or a ring mold, and arrange grilled shrimp neatly on top.
Finish with extra Parmesan, fresh basil leaves, and a squeeze of lemon.
Serve immediately while warm and fresh.