01 - Pat the salmon fillets completely dry with paper towels. Generously season both sides with salt and black pepper, pressing gently to adhere.
02 - Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat until shimmering. Place salmon fillets skin-side down if using skin-on. Sear undisturbed for 4 minutes until golden crust forms. Carefully flip and cook 2–3 minutes more until just cooked through. Transfer to a plate and cover loosely with foil to rest.
03 - Reduce heat to medium. Add remaining 1 tablespoon butter to the same skillet. Add minced garlic and chopped shallot; sauté 1–2 minutes until fragrant and translucent, taking care not to brown or burn the garlic.
04 - Pour in white wine or chicken broth, using a wooden spoon to scrape up any browned bits from the bottom of the pan. Let simmer for 2 minutes until slightly reduced and the raw alcohol smell dissipates.
05 - Stir in heavy cream and grated Parmesan cheese. Simmer 2–3 minutes, stirring constantly, until sauce thickens enough to coat the back of a spoon. The sauce should have a velvety consistency.
06 - Add fresh lemon juice, chopped parsley, and dill. Stir to combine. Taste and adjust seasoning with additional salt and pepper as needed.
07 - Return salmon fillets to the skillet, spooning the creamy sauce generously over the top. Simmer gently for 1–2 minutes just to reheat the fish. Serve immediately on warmed plates, garnished with extra fresh herbs if desired.