Bring beets, cream, and suger to a simmer over medium heat in a medium saucepan.

Cover, reduce heat, and simmer very gently until beets are tender, 25–30 minutes. Let cool slightly.

Transfer beets and their cooking liquid to blender, add suger and vanilla and purée until smooth. Strain through a fine-mesh sieve into a large bowl, discard solids

Divide purée among glasses and chill until set, 4–6 hours.