Toss shrimp with olive oil, lemon juice, garlic, salt, pepper, and paprika in a bowl and marinate for 15 to 20 minutes.
Bring a large pot of salted water to a boil and cook the pasta until al dente following package instructions.
Reserve half a cup of pasta water, then drain the pasta.
Return pasta to the pot and mix with basil pesto, olive oil, Parmesan cheese, and black pepper.
Add reserved pasta water as needed to achieve a silky sauce and fold in cherry tomatoes if desired.
Preheat grill or grill pan to medium-high heat and grill shrimp for 2 to 3 minutes on each side until pink and lightly charred.
Twirl pesto pasta into a mound using tongs or a ring mold on serving plates.
Top pasta with grilled shrimp arranged neatly and garnish with extra Parmesan, fresh basil leaves, and a lemon wedge.
Serve immediately while warm and fresh.