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 nonstick skillet over medium-high heat until shimmering. Place the salmon fillets in the skillet and sear for 4 to 5 minutes per side, or until the fish reaches your preferred level of doneness. Transfer the fillets to a warm plate and tent loosely with foil.
03 - Reduce the heat to medium. In the same skillet, melt the butter. Add the minced garlic and sauté for approximately 1 minute until fragrant, taking care not to let it brown.
04 - Pour in the heavy cream and bring to a gentle simmer. Stir in the lemon zest, lemon juice, and Dijon mustard. Continue to simmer for 3 to 4 minutes, stirring occasionally, until the sauce has slightly thickened and coats the back of a spoon.
05 - Stir in the chopped fresh parsley and adjust the seasoning with additional salt and pepper to taste.
06 - Return the salmon fillets to the skillet, spooning the lemon cream sauce generously over each piece. Simmer together for 2 to 3 minutes to allow the flavors to meld. Serve immediately, garnished with extra parsley or lemon slices if desired.