In a mixing bowl, combine warm milk, yeast, and sugar. Let it sit for 10 minutes until frothy.

In another bowl, whisk together egg, vegetable oil, ube halaya, and optional ube extract until smooth.

Gradually mix the yeast mixture into the ube mixture. Add salt and flour, mixing until a soft dough forms.

Knead the dough for 8-10 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise for about 1 hour.

Divide the risen dough into 16 pieces, flatten, place cheese in the center, and seal tightly.

Roll each ball in breadcrumbs and arrange on a baking tray. Cover and let rise for 30-40 minutes.

Preheat oven to 350°F (175°C) and bake rolls for 18-20 minutes until golden brown.

Cool on a wire rack for about 10 minutes before serving warm.