Combine the carrots with the butter, brown sugar, cayenne, and water in a medium saucepan. Stir to blend the ingredients thoroughly.
Bring the mixture to a boil over high heat. Reduce the heat to medium-low and continue boiling (uncovered) for about 20 to 25 minutes, or until carrots are tender and the liquid has evaporated. Check and stir frequently to avoid scorching. Add more water, as needed.