Bring a large pot of salted water to a rolling boil. Add the fettuccine and cook according to package instructions, around 8-10 minutes, until al dente. Drain and toss with olive oil to prevent sticking.

Pat the salmon dry and season both sides with paprika, Italian seasoning, salt, and pepper. Heat olive oil and butter in a skillet over medium heat, place the salmon skin-side down, and sear for 3-4 minutes. Flip and cook for another 3-4 minutes, drizzle with lemon juice before removing from skillet.

In the same skillet, melt an additional tablespoon of butter. Sauté minced garlic until fragrant, then pour in heavy cream and broth. Simmer for 3-4 minutes until thickened. Stir in Parmesan, crushed red pepper flakes, salt, and pepper.

Add the drained fettuccine to the skillet and toss until coated, adding reserved pasta water if necessary to achieve desired consistency.

Plate the pasta, placing a salmon fillet on top, and garnish with parsley, extra Parmesan, and crushed red pepper flakes. Serve immediately.