01 - Pat salmon fillets completely dry with paper towels. Generously season both sides with salt and black pepper.
02 - Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add salmon fillets skin-side down and sear for 4 minutes until golden. Flip carefully and cook 2–3 minutes more until just cooked through. Transfer to a plate and cover loosely with foil to keep warm.
03 - Reduce heat to medium. Add remaining 1 tablespoon butter to the same skillet. Sauté garlic and shallot for 1–2 minutes until fragrant and translucent, taking care not to brown them.
04 - Pour in white wine or chicken broth, using a wooden spoon to scrape up any browned bits from the bottom of the pan. Simmer for 2 minutes until slightly reduced.
05 - Stir in heavy cream and grated Parmesan cheese. Simmer for 2–3 minutes, stirring constantly, until sauce coats the back of a spoon and thickens nicely. Add lemon juice, parsley, and dill. Taste and adjust seasoning with additional salt and pepper if needed.
06 - Return salmon fillets to the skillet, spooning the creamy sauce generously over each piece. Simmer gently for 1–2 minutes just to reheat the fish. Serve immediately, garnished with extra fresh herbs if desired.