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. Add the salmon fillets and sear for 4 to 5 minutes per side, or until cooked to your desired doneness. Remove from the skillet and keep warm.
03 - Reduce the heat to medium and melt the butter in the same skillet. 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. Simmer for 3 to 4 minutes, stirring occasionally, until the sauce has slightly thickened.
05 - Stir in the chopped parsley and adjust the seasoning with salt and pepper to taste.
06 - Return the salmon fillets to the skillet, spooning the sauce over the top. Simmer for 2 to 3 minutes to allow the flavors to meld together. Serve immediately, garnished with extra parsley or lemon slices if desired.