Combine smoothie ingredients in a high speed blender and blend until smooth. *See Notes for tips on using a regular blender.
Pour into serving glasses and sprinkle with coconut and walnuts, if desired.
If you don't have a high speed blender:Grate the carrots instead of slicing them. Combine only the milk and shredded carrot in the blender first, and blend until smooth. If the texture still isn't as smooth as you would like, pour it through a piece of cheesecloth or a strainer to remove the pulp (catching the carrot liquid in a bowl). Then return the liquid to the blender, and add the remaining smoothie ingredients. Blend until smooth.