Warm the water in the microwave for 35 seconds. Add the active dry yeast and sugar. Mix and let sit for 5 minutes until bubbles form. Add mixture into the 1 cup flour and let it sit for forty-five minutes.
Place the hook attachment in your electric mixer. When the yeast mixture is ready, place flour and salt in the small bowl and mix using a wire whisk. Warm the milk for 45 seconds and then place the warm milk, melted butter, egg, ube flavor, and sugar into the stand mixer bowl. Mix for one minute and add the yeast mixture and flour mixture. Mix using the hook attachment until ingredients are incorporated. Mix for seven minutes.
Sprinkle flour on the working surface and transfer the dough and form into a ball. Place dough in a greased bowl and let sit, covered with cloth, at a warm temperature for 1 hour.
When ready, divide the dough into two and divide again into four using the dough cutter. You can also cut dough and weigh 60 grams each and using your palm flatten and fill with the monggo filling. Make sure that it is sealed. ( it is ok not to weigh the dough, just try to form equal shape bread. (please see the above post on how to make the filling).
Cover the dough with a damp cloth and let sit for another 30 minutes. Brush the dough with the egg wash and sprinkle with sesame seeds.
Preheat the oven to 350 F and place the bread on a baking sheet and bake for twenty minutes.