In a wide frying pan, combine wine, broth and butter. Bring to a boil over high heat. Add carrots; reduce heat, cover, and simmer, stiring occasionally until carrots are tender when pierced (10 to 15 minutes).
Uncover pan, bring cooking liquid to a boil over high heat. Boil, uncovered, stirring often, until liquid evaporates and the carrots begin to brown (about 10 minutes).