In a small saucepan, place the chopped carrots, filtered water and lemon juice over medium heat. Cook the carrots for 4-5 minutes, or until carrots soften.
Transfer carrots and liquid to a glass and place in the freezer for 10 minutes to chill.
To a high speed blender, add the pineapple, banana, turmeric and vanilla; process on high speed until smooth and creamy. Add the chilled carrot-lemon mixture and ice cubes and process again until smooth and creamy. Drink chilled.