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 tent loosely 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 30 seconds until fragrant, being careful not to brown it.
04 - Pour in the heavy cream and whisk in the Dijon mustard. Bring to a gentle simmer and cook for 3–4 minutes, stirring frequently, until the sauce begins to coat the back of a spoon.
05 - Stir in the lemon juice and lemon zest. Season with salt and freshly ground black pepper to taste. Continue simmering for 2 more minutes until the sauce slightly thickens.
06 - Fold in the chopped parsley. Taste the sauce 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 gently for 1–2 minutes to rewarm the fish through. Serve immediately, garnished with additional parsley and lemon wedges alongside.