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 fillets skin side down (if using skin-on) and cook for 4–5 minutes per side until golden brown and 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 2 more minutes until the sauce has slightly thickened.
06 - Fold in the freshly chopped parsley. Taste the sauce and adjust the lemon juice, salt, and pepper as needed.
07 - Return the salmon fillets to the skillet and spoon the sauce over the top. Simmer gently for 1–2 minutes to reheat the fish through. Serve immediately, garnished with extra parsley and lemon wedges if desired.