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 the salmon fillets skin side down if using skin-on, and cook for 4 to 5 minutes per side until golden brown and just cooked through. Transfer to a plate and loosely tent with foil to keep warm.
03 - In the same skillet, reduce the heat to medium and melt the butter. Add the minced garlic and sauté for 30 seconds until fragrant, being careful not to brown it.
04 - Stir in the heavy cream and Dijon mustard. Bring to a gentle simmer and cook for 3 to 4 minutes, stirring frequently to prevent scorching.
05 - Stir in the lemon juice and lemon zest. Season to taste with salt and freshly ground black pepper. Continue simmering for 2 more minutes until the sauce has slightly thickened.
06 - Stir 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 for 1 to 2 minutes to gently reheat the fish. Serve immediately, garnished with extra parsley and lemon wedges if desired.