Fill a large pot with water, salt generously, and bring to a boil over high heat.

Remove lobster meat from shells by cutting down the top of the shell with kitchen scissors. Pat the meat completely dry with paper towels.

Heat 1 tablespoon butter and olive oil in a wide skillet over medium-high heat. Sear lobster tails 2–3 minutes per side until just opaque. Season with salt and pepper. Remove and set aside on a cutting board.

Reduce heat to medium. Add 3 tablespoons butter to the same pan. Once melted, add minced garlic and cook for about 60 seconds until fragrant but not browned.

Pour in the heavy cream slowly while stirring. Bring to a gentle simmer and let it cook for 2–3 minutes.

Remove pan from heat briefly. Stir in Parmesan cheese a handful at a time until smooth. Add nutmeg, taste, and adjust salt and white pepper.

Cook fettuccine in the boiling salted water to just under al dente. Before draining, scoop out 1/4 cup pasta water and set aside.

Drain pasta and add it to the sauce. Toss over low heat for 1–2 minutes, adding a splash of pasta water if needed to loosen the sauce.

Slice lobster into chunky pieces and fold gently into the pasta. Serve immediately with fresh parsley and a lemon wedge if desired.