Step 1: Pat the salmon fillets dry with paper towels and season generously with salt, pepper, and a pinch of dried dill or paprika on all sides.
Step 2: Bring a large pot of salted water to a boil. Add the fettuccine and cook according to package directions until al dente. Reserve 1 cup of pasta water before draining.
Step 3: While the pasta cooks, heat 1 tablespoon of olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Once hot, add the salmon fillets skin-side down (if applicable). Sear for 4-5 minutes per side, or until cooked through and easily flakes with a fork. Remove salmon from the skillet and set aside.
Step 4: In the same skillet, reduce heat to medium. Add the remaining 2 tablespoons of butter and let it melt. Add the minced garlic and sauté for 1 minute until fragrant, being careful not to burn it.
Step 5: Pour in the heavy cream and bring to a gentle simmer, stirring constantly. Stir in the Parmesan cheese until it melts and the sauce thickens slightly. Season with salt, pepper, and a pinch of red pepper flakes for a subtle kick if desired.
Step 6: Add the drained fettuccine to the skillet with the sauce. Toss to coat evenly. If the sauce is too thick, add a splash of the reserved pasta water until it reaches your desired consistency.
Step 7: Flake the cooked salmon into large pieces and gently fold it into the creamy garlic butter fettuccine. Garnish with fresh parsley or more dill. Serve immediately.