In a medium saucepan over medium heat bring carrots, milk, sugar, ginger, salt, and cinnamon to a low boil. Reduce heat to low and simmer, stirring often, for 25 minutes or until carrots are tender.
Ladle out 1/2 cup of cooking liquid and reserve. Transfer mixture to a blender (or use an immersion blender). Add butter and blend until smooth, scraping down sides of the blender as needed. If the mixture is a little think, add reserved cooking liquid, 1-2 Tablespoons at a time, and blend until desired consistency is reached. Transfer to a serving bowl, top with chives (optional), and serve.