Activate the yeast by adding it to a mixture of lukewarm water and 1/2 tbsp sugar in a small cup or bowl. Combine the ingredients and let it rest for 5-10 minutes or until it bubble and double/triple in size.
While the yeast rests, mix the milk, 1/4 cup sugar, salt, and 3 tbsp softened butter into a microwave-safe bowl or saucepan. You can either heat it on a low fire or microwave for 1 minute.
Combine 2 cups flour, one beaten egg, and the yeast mixture in a mixing bowl. Add the milk mixture and 1 cup flour. Continue kneading by hand or use a stand mixer a medium to low speed.
Add more flour if needed (depending on dough consistency), one tbsp at a time while continue kneading until the dough becomes smooth but still slightly sticky. ( I added about 4-5 tbsp extra flour).
Transfer the dough into a greased bowl and cover it. Have the dough rest in a warm place for 1-2 hours or until it doubles in size.
Once the size is doubled, release the air pockets by punching the dough. Transfer the dough to a floured surface. Flatten it out and roll into a log. Then divide the log equally into 16-18 pieces.
Flatten out each dough piece into an oblong shape and spread the ube jam on them. Fold and seal each end and continue rolling until the log is about 10-12 inches then roll into a coil.
Lightly butter/grease the mold. Place one dough in each mold then transfer the mold in a large baking pan. Cover and let the dough rise for another 45 minutes to 1 hour.
Lightly brush the pieces with egg wash then bake in a preheated oven at 350 F for about 18-20 minutes or until top is golden. Once baked, lightly brush with melted butter while still warm.
In a small bowl, combine 1/2 cup softened butter and powdered sugar. Once itss firm, spread buttercream over cooled bread and sprinkle some sugar. Top with as much cheese as you'd like.