First clean your fish fillets with fresh water. Pat dry on both sides.
Heat a large skillet over medium-high heat. When the pan is hot, add butter (or oil) and swirl until pan is covered or butter melted.
Add the salmon fillets to the pan, flesh side down.
Pan sear the salmon flesh side down for 3 minutes, then flip with a spatula or tons to sear the skin. If your goal is a super crispy skin, use a flat spatula to gently press down on the flesh until the fillet flattens out a little more, sealing the skin against the pan. When the flesh feels firm to the touch (3-5 minutes), the salmon is ready.
Depending on the thickness of your fillet, the searing time could take longer. Check to make sure the inside is no longer pink but opaque.
Remove pan from heat and cool the salmon in the pan for 2-3 minutes. The salmon should continue cooking (a tad) off the heat. Sprinkle the flesh side of the fillets with a little salt/pepper.
Top with lemon and avocado gremolata, serve, and enjoy!