Combine the carrots, sugar, and water in a large saucepan over medium heat. Cover and simmer 20 minutes until the carrots are tender. Drain, reserving some of the liquid, and set aside.
Whisk the flour, salt, pepper, nutmeg, and milk in a smaller saucepan. Cook over medium-high heat, stirring constantly until the sauce thickens.
Puree the cooked carrots and white sauce in a blender until smooth. Add the reserved liquid to achieve a desired consistency.
Ladle into bowls and garnish with parsley. Serve immediately.
