01 - Pat salmon fillets dry with paper towels and season both sides evenly with salt and pepper.
02 - Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat until butter foams.
03 - Place salmon fillets in skillet skin-side down if using skin-on. Sear for 4 minutes, then flip and cook 2–3 minutes more until golden and just cooked through. Transfer to plate and cover loosely with foil.
04 - Reduce heat to medium. Add remaining 1 tablespoon butter to skillet. Add garlic and shallot, sautéing 1–2 minutes until fragrant but not browned.
05 - Pour in white wine or chicken broth, scraping up browned bits from bottom. Simmer 2 minutes to reduce slightly.
06 - Stir in heavy cream and Parmesan cheese. Simmer 2–3 minutes while stirring constantly until sauce thickens and coats back of spoon.
07 - Add lemon juice, parsley, and dill. Taste and adjust seasoning with additional salt and pepper if needed.
08 - Return salmon fillets to skillet, spooning sauce generously over top. Simmer gently 1–2 minutes to reheat. Serve immediately with extra herb garnish if desired.