Prep the Ube - Peel and dice the fresh ube and boil in a pot of water until tender. Drain and mash the ube until smooth using a fork or potato masher. Set aside to cool. - If fresh ube is unavailable, frozen or powdered ube can be used instead. Be sure to follow the package instructions for preparation.

Make the Ube Puree - Add the cooled mashed ube to a blender along with the coconut milk and agave nectar. Blend until smooth and creamy. -

Muddle the Lime Juice - In a separate glass, muddle the lime juice using a muddler or the back of a wooden spoon until fragrant. - If you don't have a muddler, a wooden spoon will work just as well.

Combine the Ingredients - Add the muddled lime juice, ice cubes, and ube puree to the blender. Blend until smooth and frothy. -

Serve and Garnish - Pour the cocktail into glasses and garnish with lime wedges and ube chips. - For a slushier texture, use crushed ice instead of ice cubes.