If using fresh ube, peel and grate it. If using ube powder, rehydrate according to package directions, ensuring it's smooth and free of lumps.

In a large non-stick pot or wok, combine the prepared ube, condensed milk, evaporated milk, granulated sugar, salt, and half (1/4 cup) of the unsalted butter.

Cook over medium-low heat, stirring constantly with a wooden spoon or heat-proof spatula. This continuous stirring is vital to prevent the mixture from sticking to the bottom and burning, and to achieve a smooth texture.

Continue cooking and stirring for 30-40 minutes, or until the mixture thickens considerably, pulls away from the sides of the pot, and forms a thick, glossy paste. The exact time may vary based on heat and moisture content of the ube.

Once thickened, stir in the remaining 1/4 cup of butter and the vanilla extract (if using) until fully incorporated and melted, contributing to the richness and sheen of the halaya.

Remove the pot from the heat. Transfer the hot ube halaya into a greased mold (such as a loaf pan or an aluminum tray) or a serving dish. Press down firmly with the back of a spoon or spatula to create an even, compact surface.

Let the ube halaya cool completely at room temperature, then cover it and chill in the refrigerator for at least 2-4 hours, or preferably overnight. Chilling allows it to firm up and makes it easier to slice or serve.

Serve chilled, optionally garnished with grated cheese, toasted coconut flakes, or a dollop of whipped cream.