In a small bowl, combine warm water, active dry yeast, and one tablespoon of sugar. Stir gently and let it sit for about 5 minutes until bubbly and frothy.

In a large mixing bowl, add the activated yeast mixture, softened butter, eggs, remaining sugar, warm milk, mashed ube, liquid ube flavoring, and salt. Mix everything until fully incorporated.

Gradually add 3 cups of all-purpose flour into the mixture, stirring until a shaggy mass forms. Reserve some flour for kneading.

Lightly oil your work surface and transfer the dough onto it. Knead the dough for about 8-10 minutes until smooth and elastic. Place in a greased bowl, cover it, and let rise for 1.5 to 2 hours.

Punch down the risen dough and transfer it to a floured surface. Shape into a log and cut it into 14 portions. Place a cube of cheese in the center of each piece, fold over, and roll into smooth balls.

Roll each ball in bread crumbs and arrange on a lined baking sheet. Cover and let rise for another 30-60 minutes.

Preheat your oven to 350°F. Place the rolls in the oven and bake for 20-23 minutes until golden brown.

Allow the rolls to cool on the baking sheet for about 10 minutes before transferring to a wire rack. Serve warm.