In a large skillet set to medium heat, add carrots. Pour water and cooking wine over carrots. Bring to a boil then reduce heat to medium-low. Cover and simmer for 10-15 minutes, or until carrots are tender. Drain any excess liquid. Place carrots in a separate dish; set aside.
In the same skillet, melt butter over medium-low heat. Add honey, brown sugar and nutmeg. Cook, stirring, until sugar is dissolved. Stir in carrots, coating well in butter-sugar mixture. Continue cooking, gently stirring, until carrots are hot and glazed. Remove from heat and stir in chopped parsley. Serve immediately.