In a large mixing bowl, combine warm milk, melted unsalted butter, room-temperature egg, vanilla extract, and ube extract. Add rapid-rise yeast and mix well.

In a separate bowl, whisk together bread flour, sugar, and kosher salt. Gradually add to wet ingredients, stirring until a shaggy dough forms.

Cover the bowl with a kitchen towel and let it rest for about 20 minutes to hydrate.

Knead the dough on a floured surface for about 7 minutes until smooth and elastic.

Place dough in a greased bowl, cover, and let it rise for about 2 hours or until doubled in size.

Gently punch down the risen dough and divide it into 20 equal portions, shaping them into balls.

Flatten each ball slightly, place a cheese cube or ube halaya in the center, and fold the edges to seal.

Roll each filled ball in breadcrumbs and place on a parchment-lined baking tray.

Cover the tray with a towel and let the shaped buns rise for an additional 30 minutes.

Preheat the oven to 350°F (175°C). Bake for 18-20 minutes until golden brown.

Remove from the oven and cool on a wire rack for about 10 minutes before serving.