Wash the purple sweet potato or real ube thoroughly.
Place it in a pot and cover with water.
Boil until completely soft and fork-tender.
Drain the water and allow it to cool slightly.
Peel off the skin.
Grate the cooked kamote or ube until smooth.
In a large bowl, combine the grated kamote, evaporated milk, condensed milk, and powdered milk.
Mix until evenly combined.
Transfer the mixture into a non-stick pan.
Cook over low heat while stirring continuously.
Continue stirring until the mixture thickens.
Once the mixture starts pulling away from the sides of the pan, add the butter.
Keep stirring until the halaya becomes smooth, shiny, and no longer sticks to the pan.
Transfer into serving containers or molds.
Top with latik, grated cheese, or butter if desired.
Let cool completely before serving.
Chill before serving for an even firmer texture.