Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add ube, cover, and steam until tender, about 20 minutes. Cool until easily handled and cube. Measure 1/4 cup of the cooked ube.
Combine 1/4 cup ube, milk, and vanilla ice cream in a blender; blend until smooth.