Place oven rack 7 or 8 inches from the broiler element and turn on broiler.
Place butter into a cast iron skillet or other heavy oven safe skillet and melt over medium heat. Stir the butter around until the milk solids start to caramelize, then lower the heat to low. Keep stirring while the butter starts to get a brown color and you may notice a slightly nutty aroma, (5 or 6 minutes).
Stir in the minced garlic cook until fragrant, 30 to 45 seconds. Salt and pepper the salmon, then add to the skillet, skin down. Baste the salmon with the butter using a spoon by tipping the skillet to get a nice spoonful. Do this every minute or so. Cook the salmon until it is nearly halfway cooked through, 7 minutes.
Put 1 tablespoon of honey in a small bowl and add a spoonful of hot butter from the skillet. Stir to thin the honey. Drizzle about half of the honey over the top of the salmon fillets. Place the skillet under the broiler.
Broil for 2 minutes keeping an eye on the salmon so that the honey does not burn. Remove from the oven and drizzle the salmon with the remaining honey. Cover the skillet with a lid for 2 minutes to finish the cooking and to rest the salmon.