If using fresh whole 2 lb ube (purple yam) fresh or frozen grated; if using whole fresh ube, boil until tender then grate, scrub and boil in a large Pot of water for 30–40 minutes until fork-tender. Drain, peel, and grate finely using a Grater. If using pre-grated frozen 2 lb ube (purple yam) fresh or frozen grated; if using whole fresh ube, boil until tender then grate, thaw completely and squeeze out any excess moisture with a clean Kitchen Towel.

In a large Skillet or wide heavy-bottomed Skillet, combine the grated 2 lb ube (purple yam) fresh or frozen grated; if using whole fresh ube, boil until tender then grate, 1 can coconut milk full-fat, well shaken, 1 can evaporated milk, and 1 can sweetened condensed milk over medium heat. Stir well to combine. Bring to a gentle simmer, stirring frequently to prevent sticking.

Reduce heat to medium-low and continue cooking, stirring constantly with a Wooden Spoon or Spatula, for 30–40 minutes. The mixture will gradually thicken and pull away from the sides of the Skillet. Keep stirring — this is the key step that gives ube halaya its smooth, jammy texture.

Once the mixture is very thick and holds its shape when you drag the Wooden Spoon across the bottom of the Skillet, add the 4 tbsp unsalted butter cut into pieces pieces, ¼ tsp fine sea salt, and 2 lb ube (purple yam) fresh or frozen grated; if using whole fresh ube, boil until tender then grate (if using). Stir vigorously until the 4 tbsp unsalted butter cut into pieces is fully incorporated and the halaya is glossy and smooth.

Transfer the ube halaya into a lightly greased Mold, Mixing Bowl, or individual Ramekins. Smooth the top with a Spatula. Brush the surface with a little 1 tbsp butter melted, brushed on top before serving for a glossy finish and garnish with 2 tbsp shredded coconut toasted, optional garnish if desired. Let cool to room temperature, then refrigerate for at least 1 hour before serving.