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 shimmering. Place the salmon fillets in the pan 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. Melt the butter in the same skillet, then sauté the minced garlic for about 1 minute 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 coats the back of a spoon.
05 - Fold in the chopped parsley and taste the sauce. Adjust seasoning with additional salt and pepper as needed.
06 - Return the salmon fillets to the skillet, spooning the sauce generously over each piece. Let everything simmer together for 2 to 3 minutes so the flavors marry.
07 - Transfer to serving plates immediately. Garnish with extra fresh parsley or thin lemon slices if desired.