Bring a large pot of salted water to a boil, then add the linguine. Cook according to package instructions, usually about 9-11 minutes, until al dente. Drain and reserve a small cup of pasta water.

In a large skillet, heat 2 tablespoons of olive oil over medium heat. Season salmon filets with kosher salt and pepper. Sear for about 5 minutes until golden-brown.

Flip the salmon filets and cook for an additional 12-15 minutes until the fish flakes easily. Transfer to a plate and reduce heat.

In the same skillet, add 2 tablespoons of unsalted butter. Once melted, add minced garlic and sauté for 30-45 seconds until fragrant.

Pour in 1 cup of heavy cream and 1/2 cup of chicken broth, along with lemon juice. Stir and bring to a low simmer, cooking until slightly thickened.

Stir in 1/2 cup of grated Parmesan cheese and chopped parsley, cooking for another 1-2 minutes until the cheese melts.

Add the drained linguine and toss gently to coat. If the sauce is too thick, add a splash of reserved pasta water. Mix in the salmon, breaking it into chunks.

Plate the salmon pasta hot, garnishing with extra Parmesan and parsley.