Brush a large bowl with oil and set aside until ready to use. Brush also a round mold with nonstick oil and set aside.
Brush pan and bowl with melted butter and set aside.
Mix flour, sugar, and salt in a large size bowl and make a well in the middle. Add the proofed yeast, egg, Ube flavor, and the water roux mixture. Mix and when you've formed a dough that looks like mud, add the butter.
Mix on medium for seven minutes,Note that this will be a very wet dough, it will be hard to work on it, so you need to coat your hands with flour. Transfer the dough to an oiled bowl and cover it with a cloth or plastic wrap and let rise in a warm place for an hour.
When ready, punch the dough twice and work on a floured surface. Form a circle and divide it into 8 pieces (depending on the size of the Ube Ensaymada you want). Always have the flour handy so that you can coat and sprinkle a small amount of it when you are working on the dough, since it is very soft and wet. Form each piece into a ball and flatten it in between your hand and fill it with the Ube Halaya, and seal the dough. Or, you can form the dough into a 4x6 rectangle. put the filling and roll it to one end and shape it into a disk. Fill a small amount of filling when doing this, so that the bread will not puff during baking. Place the filled dough into the prepared mold. Cover and let rise for another 30 minutes.
Preheat the oven to 350 F and bake for twenty-two minutes. Let cool and frost.