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 warm plate and set aside.
03 - Reduce heat to medium. In the same skillet, melt the butter and 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, fresh lemon juice, and Dijon mustard. Continue simmering for 3 to 4 minutes, stirring occasionally, until the sauce slightly thickens and coats the back of a spoon.
05 - Stir in the chopped parsley and adjust seasoning with salt and pepper to taste.
06 - Return the salmon fillets to the skillet and spoon the lemon cream sauce generously over each portion. Simmer together for 2 to 3 minutes allowing the flavors to meld. Serve immediately, garnished with additional fresh parsley or lemon slices if desired.