Make the sauce first: Place butter in a small (light colored) saucepan. Cook over medium heat, swirling pan occasionally, until butter is fragrant and has turned nice and brown. Get out your blender. Remove butter from heat and pour it immediately into the blender (you want it to stop cooking). Add the lime juice, garlic, and salt and pepper to a blender. Blend on low speed for 30 seconds to 1 minute until well combined. Set aside.
Pat both sides of the salmon dry. Line the fillets up on a large cutting board and salt and pepper the top sides. Sprinkle the tops with flour, about 1 teaspoon per fillet, or just eyeball it. Then drizzle with honey, about 3/4 teaspoon per fillet (again, just eyeball it).
Heat 1 tablespoon of olive oil over medium heat in the largest skillet that you have, and swirl to coat. When the oil shimmers, add the fillets, flour side down. Don't crowd them! You don't want them to steam each other. If you don't have a big enough pan, do it in batches or use two pans.
Set a timer for about 3 minutes. Meanwhile, treat the other side of the salmon that is now facing up: salt and pepper, flour, then honey. Flip the salmon when it is nice and brown. It should take 3-5 minutes per side, depending on the thickness of your salmon.
Plate salmon immediately. Blend the browned butter sauce one more time, since it has probably separated by now, and drizzle each fillet with 1 or 2 tablespoons sauce. Sprinkle with lime zest. Enjoy!