Marinate Shrimp: In a medium bowl, combine thawed large shrimp with olive oil, lemon zest, parsley, minced garlic, sea salt, and pepper. Toss until well coated and let marinate for about 20 minutes.

Cook Spaghetti: Bring a large pot of salted water to a boil. Add spaghetti and cook until al dente, usually about 8-10 minutes. Reserve a cup of pasta water, then drain and set aside.

Sear Shrimp: Heat a skillet over medium-high heat and add olive oil. Sear marinated shrimp for about 2 minutes on each side until pink and opaque. Remove and keep warm.

Prepare Sauce: In the same skillet, reduce heat to medium and whisk together lemon juice, extra lemon zest, Parmigiano-Reggiano cheese, and parsley until smooth. Season with salt and pepper to taste.

Combine Pasta and Sauce: Pour sauce over drained spaghetti. Toss gently to combine, adding reserved pasta water as needed to achieve desired consistency.

Serve: Transfer to a serving platter, top with seared shrimp, garnish with parsley and olive oil. Optionally pass extra grated cheese at the table.