Ube is a purple yam, a root crop that grows mostly everywhere in the Philippines. The most popular way of cooking ube is to make it into halaya hence called Ube Halaya. The taste and texture is really neat - it comes across as a heavy custard type pudding. It may be eaten by itself or as an ingredient in other deserts like Halo-Halo.
The traditional way of cooking ube halaya is to boil the ube, peel off the skin and grate the meat. Put butter in a saucepan over medium fire. Add the ube, and the fresh and evaporated milks. Mix all the ingredients very well. Continuously stir the mixture; never leave it unattended, until it turns thick. Adding sugar is optional.