In a medium-size mixing bowl, add the whole milk, water, egg, and ube flavoring. Whisk until combined.
In a separate bowl, mix the all-purpose flour, instant yeast, sugar, and kosher salt. Combine well.
Make a well in the center of the flour mixture, and slowly pour in the ube mixture
Using a stand mixer, add butter and slowly combine the ingredients until a dough starts to form
Dust cooking surface with flour. Place ube dough on the surface and knead until dough is smooth and elastic (about 10 minutes).
Apply cooking spray to a new large mixing bowl. Place ube dough in the bowl and cover. Leave to proof and double in size, about one hour.
Portion dough into 12 pieces, each sized like a small bun. Roll each piece into a smooth ball then flatten and place a cheese cube in the center. Bunch edges around cheese and pinch to seal at the top. Roll again and coat in bread crumbs. Repeat for all remaining buns.
Line baking sheets with parchment paper and cooking spray. Arrange dough balls on sheets and cover with plastic wrap. Proof again until doubled in size, about one hour.
Preheat oven to 350°F (180°C)
Uncover baking sheets and transfer to the preheated oven. Bake for 15-20 minutes, until slightly browned on top. Remove from oven and leave to cool for 15 minutes. Enjoy immediately.