In a medium saucepan, combine ½ cup unsalted butter, 1 cup whole milk, 1 cup water, 2 tablespoons sugar, and a pinch of salt. Bring to a rolling boil over medium heat.

Remove from heat and add 1 cup all-purpose flour, stirring until the dough pulls away from the sides and forms a ball.

Let the pastry cool for about 5 minutes, then add 4 large eggs, mixing well after each addition until glossy.

Using a piping bag, pipe 2-inch rounds onto a baking sheet lined with parchment paper, spaced 2 inches apart.

Preheat oven to 400°F (200°C) and bake for 10 minutes, then reduce to 350°F (175°C) for an additional 20 minutes until golden brown.

Cool completely on a wire rack.

In a saucepan, whisk together 1 cup ube halaya, ½ cup whole milk, ½ cup heavy cream, ¼ cup sugar, and 2 tablespoons cornstarch over medium heat until thickened.

Remove from heat, stir in 2 egg yolks and 1 teaspoon vanilla extract, then let cool.

Poke a small hole in the bottom of each puff, fill with the ube filling using a piping bag.

Dust with powdered sugar and serve chilled or at room temperature.