Pat the salmon dry. Season both sides with salt and pepper. Dry fish sears better, so don’t skip this step.
Sear the salmon. Heat olive oil in a large skillet over medium-high.
Add salmon, skin-side down if using. Cook 3–4 minutes per side until golden and just cooked through. Transfer to a plate and tent loosely with foil.
Lower the heat and build flavor. Reduce heat to medium.
Add butter to the same pan. Stir in shallot and cook 1–2 minutes until translucent. Add garlic and cook 30 seconds, just until fragrant.
Deglaze. Pour in white wine.
Scrape up any browned bits with a wooden spoon. Simmer 2–3 minutes until reduced by about half.
Make it creamy. Stir in broth, heavy cream, Dijon, and red pepper flakes if using. Simmer gently 3–5 minutes until slightly thickened.
Avoid a hard boil to keep the sauce smooth.
Add brightness. Stir in lemon zest, lemon juice, and Parmesan if using. Taste and season with salt and pepper. The sauce should be balanced—rich, savory, and lightly tangy.
Return the salmon. Nestle the fillets into the sauce.
Spoon sauce over the top and warm for 1–2 minutes. Sprinkle with fresh parsley or dill.
Serve. Plate with extra lemon wedges. Great with pasta, rice, mashed potatoes, or sautéed spinach.