In a medium saucepan, combine ½ cup of unsalted butter, 1 cup of whole milk, ½ cup of water, 1 tablespoon of sugar, and ¼ teaspoon of salt. Bring this mixture to a boil over medium heat, stirring occasionally. Once it reaches a boil, quickly add 1 cup of all-purpose flour and stir vigorously until the dough forms a smooth ball that pulls away from the sides of the pan, about 2-3 minutes.

Remove the saucepan from heat and let the dough cool for about 5 minutes. Then, add 4 large eggs, one at a time, stirring well after each addition until the dough becomes glossy and smooth.

Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper or a silicone mat. Using a piping bag fitted with a large round tip, pipe the dough into 2-inch rounds, spaced about 2 inches apart.

Place the baking sheet in the preheated oven and bake for 10 minutes. After this initial baking, reduce the temperature to 350°F (175°C) and continue baking for another 20 minutes, or until the puffs are golden brown and sound hollow when tapped.

Once baked, remove the Ube Cream Puffs from the oven and let them cool completely on a wire rack.

In a medium saucepan, whisk together 1 cup of ube halaya, ½ cup of whole milk, ½ cup of heavy cream, ½ cup of sugar, 2 tablespoons of cornstarch, and 2 egg yolks. Cook over medium heat until thickened and bubbly, about 5-7 minutes.

Once the Ube Cream Filling is chilled, use a small sharp knife to cut or poke a hole in the bottom of each cooled cream puff. Fill a piping bag with the ube cream and carefully pipe it into each puff until they feel full and slightly heavy.

Optionally, dust the filled Ube Cream Puffs with powdered sugar for a touch of sweetness and a beautiful presentation.