Pour the coconut milk in a cooking pot. Bring to a boil.
Once the coconut milk start to boil, add the sugar. Stir until the sugar dilutes completely.
Put-in the grated purple yam. Continue to cook while stirring (using low to medium heat) until the texture gets thick. Note: It will take around 20 to 30 minutes. Please be patient.
Grease the llanera with cooking oil. Transfer the ube halaya to the greased llanera to mold it into shape.
Let it cool down to room temperature. You can serve it immediately of place it in the refrigerator (covered with cling sap).