Bring a large pot of salted water to a rolling boil over high heat. Add the fettuccine and cook for 8-10 minutes until al dente. Drain the pasta and toss with olive oil to prevent clumping.

Season the salmon fillets with salt and pepper. Heat a skillet over medium-high heat and add olive oil. Sear the salmon skin-side down for 3-4 minutes until crispy. Flip and cook for another 3-4 minutes, then drizzle with lemon juice and set aside.

In the same skillet, reduce heat to medium and add butter. Once melted, add minced garlic and sauté for 30 seconds. Pour in heavy cream and chicken broth, stirring well. Let simmer for 3-4 minutes until slightly thickened, then mix in Parmesan cheese and crushed red pepper flakes.

Add the drained fettuccine to the sauce, tossing to coat. If needed, add reserved pasta water for desired consistency.

Plate the fettuccine and place a salmon fillet on top of each serving. Garnish with parsley, extra Parmesan, and red pepper flakes.