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, about 10 minutes. Purée ube in a blender or food processor, or thoroughly mash it by hand.

Combine 1 cup puréed ube, 3/4 cup whole milk, coconut milk, and sugar in a blender or food processor; blend until completely smooth.

Pour remaining 3/4 cup whole milk into a saucepan. Sprinkle gelatin on top and let stand for 5 minutes.

Heat milk-gelatin mixture over medium-low heat, stirring until gelatin is dissolved, 3 to 5 minutes. Pour in ube mixture and increase the heat to medium. Heat until steam starts to rise from the mixture, stirring occasionally, 3 to 5 minutes.

Pour mixture into individual serving glasses or molds. Transfer to the refrigerator and chill until set, about 3 hours.