01 - Pat the salmon fillets thoroughly dry with paper towels and season both sides generously with salt and freshly ground black pepper.
02 - Heat olive oil in a large skillet over medium-high heat. Place the salmon skin side down (if using skin-on fillets) and cook for 4–5 minutes per side until a golden crust forms and the fish is just cooked through. Transfer to a plate and loosely tent with foil to keep warm.
03 - Reduce the heat to medium and melt the butter in the same skillet. Add the minced garlic and sauté for about 30 seconds until fragrant, being careful not to brown it.
04 - Pour in the heavy cream and stir in the Dijon mustard. Bring to a gentle simmer and cook for 3–4 minutes, stirring frequently to prevent scorching.
05 - Stir in the lemon juice and lemon zest. Season with salt and freshly ground black pepper to taste. Continue simmering for about 2 minutes until the sauce slightly thickens.
06 - Fold in the freshly chopped parsley. Taste and adjust the lemon juice, salt, and pepper as needed to balance the flavors.
07 - Return the salmon fillets to the skillet and spoon the sauce generously over the top. Simmer for 1–2 minutes just until the fish is warmed through and coated.
08 - Serve immediately, garnished with additional chopped parsley and lemon wedges alongside if desired.