01 - Pat the salmon fillets dry with paper towels. Season both sides with salt and pepper.
02 - Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat.
03 - Add salmon fillets, skin-side down if using skin-on, and sear for 4 minutes. Flip and cook 2–3 minutes more until golden and just cooked through. Transfer to a plate and cover loosely with foil.
04 - Reduce heat to medium. Add remaining 1 tablespoon butter to the same skillet. Add garlic and shallot; sauté 1–2 minutes until fragrant but not browned.
05 - Pour in white wine (or chicken broth), scraping up any browned bits. Simmer 2 minutes to reduce slightly.
06 - Stir in heavy cream and Parmesan. Simmer 2–3 minutes, stirring, until sauce thickens.
07 - Add lemon juice, parsley, and dill. Season to taste with additional salt and pepper if needed.
08 - Return salmon fillets to the skillet, spooning sauce over the top. Simmer gently for 1–2 minutes to reheat. Serve immediately, garnished with extra herbs if desired.