Boil salted water and cook linguine until al dente. Reserve 1 cup of pasta water.
Pat shrimp dry, season with salt and pepper.
Heat oil in skillet; sear shrimp 2 minutes per side until pink. Remove and set aside.
In same skillet, sauté garlic in olive oil until fragrant.
Add pesto, cream, Parmesan, lemon zest, and juice. Stir until smooth.
Toss linguine into sauce; thin with pasta water as needed.
Return shrimp to pan, toss gently, and heat through.
Garnish with basil, Parmesan, and lemon wedges before serving.