Prep the salmon. Pat fillets very dry with paper towels. Season both sides with salt and pepper. Let sit 5 minutes while you heat the pan ÔÇö dry fish browns better.

Make the lemon garlic sauce. In a small bowl, melt the butter (microwave 20ÔÇô30 seconds) and stir in olive oil, garlic, lemon zest, lemon juice, paprika, and red pepper flakes. (This is also your lemon garlic salmon marinade if you want a short rest: spoon 2 Tbsp over the fish for 10ÔÇô15 minutes in the fridge; keep the rest for the pan.)

Sear for color. Heat 1 Tbsp olive oil in a large oven-safe skillet over medium-high. Place salmon flesh-side down (skin-side up if skin-on). Sear 2ÔÇô3 minutes until golden. Flip carefully.

Sauce and finish. Spoon most of the lemon garlic butter over the fillets. Tuck lemon slices around the pan. Transfer skillet to a 400┬░F (200┬░C) oven and bake 5ÔÇô8 minutes, depending on thickness (see chart below), until the thickest part reaches 145┬░F (63┬░C) or flakes easily with a fork and looks opaque in the center.

Rest and serve. Rest 2ÔÇô3 minutes off heat. Spoon pan sauce over the top. Sprinkle parsley. Serve hot.