Melt the butter in large sauté pan over high heat. Then reduce the heat to medium and stir in the carrot pieces. Drizzle the honey over them and sprinkle with salt and pepper. Add enough water to come about 1/3 of the way up the sides of the carrots and cover the bottom of the pan.
Reduce the heat to low, cover with a lid and simmer the carrots until almost all of the liquid has evaporated and the carrots are barely tender when a knife is inserted, 10 minutes.
Remove the lid to allow any remaining liquid to evaporate. Cook the carrots, turning regularly to brown well on all sides. Add just enough water, about 1 tablespoon, to the carrots to release the flavor from the bottom of the pan. Turn the carrots to cover with the glaze. Season with salt and pepper to taste.