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. Once the oil shimmers, add the salmon fillets and sear for 4 to 5 minutes per side until golden and cooked to your preferred doneness. Transfer to a plate and keep warm.
03 - Reduce the heat to medium and melt the butter in the same skillet. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to brown it.
04 - Pour in the heavy cream and bring to a gentle simmer. Stir in the lemon zest, fresh lemon juice, and Dijon mustard. Let the sauce simmer for 3 to 4 minutes, stirring occasionally, until it slightly thickens and coats the back of a spoon.
05 - Stir in the chopped parsley and adjust the seasoning with salt and pepper to taste.
06 - Return the salmon fillets to the skillet and spoon the sauce over the top. Simmer together for 2 to 3 minutes so the flavors meld. Serve immediately, garnished with additional parsley or lemon slices if desired.