01 - Pat the salmon fillets dry with paper towels and season both sides generously with salt and freshly ground black pepper.
02 - Heat olive oil in a large nonstick skillet over medium-high heat. 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 set aside.
03 - Reduce the heat to medium and melt the butter in the same skillet. Add the minced garlic and sauté for about 1 minute, stirring constantly, until fragrant and lightly golden.
04 - Pour in the heavy cream and bring to a gentle simmer. Stir in the lemon zest, fresh 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 - Stir in the chopped parsley and season the sauce with additional salt and pepper to taste.
06 - Return the salmon fillets to the skillet, spooning the lemon cream sauce generously over the top. Let simmer together for 2 to 3 minutes, allowing the flavors to meld and the fish to heat through.
07 - Serve the salmon immediately, garnished with additional fresh parsley or thin lemon slices if desired. Pair with steamed vegetables, rice, or creamy mashed potatoes.