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 skillet over medium-high heat. Place the salmon skin side down (if using skin-on) and cook for 4–5 minutes per side until golden and just cooked through. Transfer to a plate and loosely tent with foil to keep warm.
03 - In the same skillet, reduce heat to medium and melt the butter. Add the minced garlic and sauté for about 30 seconds until fragrant.
04 - Stir in the heavy cream and Dijon mustard. Simmer gently for 3–4 minutes, stirring frequently to prevent scorching.
05 - Add the lemon juice and lemon zest. Season with salt and freshly ground black pepper to taste. Simmer for 2 more minutes until the sauce slightly thickens.
06 - Stir in the chopped parsley. Taste and adjust the lemon juice, salt, and pepper as desired.
07 - Return the salmon fillets to the skillet and spoon the sauce over the top. Simmer for 1–2 minutes to gently reheat. Serve immediately, garnished with extra parsley and lemon wedges if desired.