01 - Pat the salmon fillets thoroughly dry with paper towels. Season both sides generously with salt and freshly ground black pepper.
02 - Heat olive oil in a large nonstick skillet over medium-high heat until the oil shimmers. Carefully place the salmon fillets in the skillet and sear for 4 to 5 minutes per side, or until the fish reaches your preferred level of doneness. Transfer the fillets to a warm plate and tent loosely with foil.
03 - Reduce the heat to medium and melt the butter in the same skillet. Add the minced garlic and sauté for approximately 1 minute, stirring frequently, until fragrant and lightly golden.
04 - Pour in the heavy cream and bring to a gentle simmer. Stir in the lemon zest, lemon juice, and Dijon mustard. Continue simmering for 3 to 4 minutes, stirring occasionally, until the sauce has slightly thickened and coats the back of a spoon.
05 - Fold in the chopped parsley and season with additional salt and pepper to taste. Stir to combine evenly.
06 - Return the salmon fillets to the skillet and spoon the sauce generously over each portion. Simmer together for 2 to 3 minutes, allowing the flavors to meld. Serve immediately, garnished with additional parsley or lemon slices if desired.