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 teaspoon flour over each side of the salmon fillets and spread flour to evenly coat.
Evenly drizzle 3/4 teaspoon honey over each side of the flour coated salmon fillets. Drizzle 1 tablespoon olive oil into a 10 inch non-stick or cast iron 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 tablespoon Browned Butter Lime Sauce and sprinkle with lime zest. Serve warm.
To Make The Browned Butter Lime Sauce: Place butter in a small (light colored to monitor browning) saucepan. Cook over medium heat, stirring pan constantly, until butter is fragrant and has turned a brownish coloring. Careful not to burn.
Remove browned butter from heat and add it, along with lime juice, garlic, salt and pepper to a blender. Blend on low speed for about 30 seconds, 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).