01 - Pat the salmon fillets thoroughly dry with paper towels. Season both sides generously with salt and freshly ground black pepper.
02 - Heat olive oil in a large skillet over medium-high heat until shimmering. 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. In the same skillet, melt the butter. 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, until the sauce begins to coat the back of a spoon.
05 - Stir in the freshly squeezed lemon juice and lemon zest. Season with salt and freshly ground black pepper to taste. Continue simmering for 2 more minutes until the sauce is slightly thickened.
06 - Fold in the 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 gently for 1–2 minutes to reheat the fish through. Serve immediately, garnished with extra parsley and lemon wedges if desired.