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. Place salmon fillets 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 - Reduce heat to medium. In the same skillet, melt the butter. Add minced garlic and sauté for about 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 thicken slightly.
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 coats the back of a spoon.
06 - Remove from heat and stir in the chopped parsley. Taste and adjust the lemon juice, salt, and pepper as needed.
07 - Return the salmon fillets to the skillet, spooning the sauce over the top. Simmer gently for 1–2 minutes to rewarm the fish. Serve immediately, garnished with extra parsley and lemon wedges if desired.