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. Puree ube in a blender or food processor, or thoroughly mash by hand.
Combine 1 cup pureed ube, 3/4 cup 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. 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 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.