Prepare the yeast: Mix the active dry yeast, sugar, and warm water. Let it sit for 5 to 10 minutes, until foamy. Skip this step if using instant yeast.
Mix the dry ingredients: Whisk the bread flour and salt in a large bowl. If using instant yeast, add it here.
Mix the wet ingredients: Add the egg, condensed milk, oil, ½ cup ube halaya, and ube flavoring to the yeast mixture. Mix until smooth. If using instant yeast, also add the water and sugar here.
Make the dough: Pour the wet mixture into the flour mixture. Stir until a sticky dough forms.
Knead: Use a stand mixer for 12 to 15 minutes, or knead by hand for 20 to 25 minutes. The dough is ready when it is smooth and stretchy.
Let it rise: Place the dough in a lightly oiled bowl. Cover and let it rise in a warm place for 1 to 2 hours, or until doubled.
Divide and fill: Press out large air bubbles. Divide the dough into 16 pieces. Flatten each piece into a 4-inch circle. Add 1 tablespoon cheese and 1 tablespoon ube halaya to the center.
Shape: Pull the edges over the filling and pinch them closed. Place seam-side down, shape into a smooth ball, and roll in breadcrumbs.
Rise again: Place the rolls on a lined baking sheet. Cover and let them rise for 30 to 45 minutes, or until puffy.
Bake: Heat the oven to 400°F (205°C). Bake for 5 minutes. Lower the heat to 350°F (175°C) and bake for 15 to 17 minutes more, until lightly golden.