Start by bringing a large pot of salted water to a boil. Add the fettuccine and cook according to the package directions until al dente. Reserve about ½ cup of pasta water, then drain the noodles and set them aside.
While the pasta cooks, heat 2 tablespoons of olive oil in a large skillet over medium heat. Add the salmon chunks to the pan, seasoning lightly with salt and pepper if desired. Sear the salmon pieces for about 2–3 minutes on each side until they are cooked through and golden. Remove the salmon from the skillet and set aside.
In the same skillet, reduce the heat to medium-low and add 2 tablespoons of butter. Once melted, stir in the minced garlic and sauté for about 30 seconds to 1 minute, just until fragrant. Be careful not to burn the garlic.
Pour in the heavy cream, stirring constantly, and bring it to a gentle simmer. Allow the cream to cook for 2–3 minutes, letting it thicken slightly. Then, stir in the grated Parmesan cheese, continuing to mix until the sauce is smooth and creamy.
Add the cooked fettuccine to the skillet, tossing it gently to coat it in the creamy sauce. If the sauce feels too thick, add a splash of the reserved pasta water until it reaches your desired consistency.
Finally, return the cooked salmon to the pan, carefully folding it into the pasta. Let everything warm through for a minute or two.
Serve immediately, garnished with extra Parmesan or fresh herbs like parsley if you like.