Use a clean rough-sided sponge to scrub and smooth the carrots and remove any peel marks (optional).
In a medium straight-sided skillet add 1 3/4 cups water, the butter, sugar, salt and star anise. Bring to a boil over high heat, then reduce the heat to medium-low. Add the carrots and gently simmer until the carrots are tender and the volume of liquid in the pan is reduced by half, about 45 minutes. Serve the carrots on a platter with the cooking liquid poured over the top.