Bring a large pot of salted water to a boil over high heat. Add linguine pasta and cook according to package instructions, stirring occasionally, until al dente, about 8-10 minutes. Drain and set aside, reserving a little pasta water.

In a large skillet, heat 1 tablespoon of olive oil over medium heat. Season the salmon filet with salt and pepper. Cook salmon skin-side up for about 5 minutes until golden brown. Flip and cook for another 12-15 minutes until cooked through. Remove from pan and set aside.

In the same skillet, melt 2 tablespoons of unsalted butter. Add 2 cloves of minced garlic and sauté for about 30 seconds until fragrant.

Pour in 1 cup of heavy cream, ½ cup of chicken broth, and the juice of one fresh lemon, stirring to combine. Bring to a low simmer for about 2-3 minutes. Stir in ½ cup of grated Parmesan cheese until melted and sauce thickens.

Add the drained linguine to the skillet and toss to coat with the sauce. Fold in the cooked salmon chunks. Add reserved pasta water if needed to adjust sauce consistency.

Plate the salmon pasta, distributing salmon and linguine evenly. Garnish with additional grated Parmesan and chopped parsley.