Working in batches of two salmon fillets at a time (or using two skillets, because you don't want to overcrowd the salmon when cooking it on the stove-top so it cooks more evenly), place salmon fillets on a cutting board or plate and sprinkle 1 tsp flour over each side of the salmon fillets and spread flour to evenly coat. Evenly drizzle 3/4 tsp honey over each side of the flour coated salmon fillets.* Drizzle 1 Tbsp olive oil into a 10 inch non-stick skillet, swirl pan to evenly coat bottom and heat over medium heat. Once oil it hot, carefully place salmon ) in pan and cook over medium heat, 3-5 minutes per side until salmon has cooked through and bottom has nicely browned. Plate salmon immediately, drizzle each fillet with 1 1/2 - 2 Tbsp Browned Butter Lime Sauce and sprinkle with lime zest. Serve warm.
*note that once you remove the salmon from the plate some of the flour and honey coating will stick to the plate so I'd recommend just scraping it up with a spatula and adding it to the salmon once it's in the pan, alternately you could just coat one side with the flour and honey then after adding it to the pan you can coat the top side with flour and honey. Either way works I'd just say don't waste any of that delicious coating.
Browned Butter Lime Sauce:
6 Tbsp salted butter, diced
3 Tbsp fresh lime juice
1 clove garlic, minced
1/2 tsp salt
1/2 tsp freshly ground black pepper
Place butter in a small (light colored) saucepan. Cook over medium heat, swirling pan occasionally, until butter is fragrant and has turned a tan shade. I would recommend not to stir constantly rather swirl pan occasionally. Remove from heat and add browned butter along with lime juice, garlic, salt and pepper to a blender. Blend on low speed for 30 seconds to 1 minute until well blended. Pour sauce into a small glass dish (note: whisk butter mixture with a fork before pouring onto salmon as it will separate, rewarm if needed).
Recipe Source: inspired by Gourmet Magazine, July 2006