In a small pot, whisk the glutinous rice flour and water over medium heat until it forms a sticky goo. This will take a couple minutes but make sure to keep whisking or else it will burn. Once it forms the blob, take it off the heat to cool.
In the bowl of stand mixer, combine the bread flour, ube powder, egg whites, sugar, yeast, salt, and the sticky blob of glutinous rice flour.
Mix on low first until everything is combined. It will look a little dry at first, but just keep mixing. Try to refrain from adding water because it will throw off the ratio of ingredients. You will have to scrape the bowl a couple times.
Once everything has come together, mix on medium/high for 5 minutes. Then add the butter and mix on high for another 15-20 minutes. The dough will look more like a paste and stick to the sides of the bowl. If you run your spatula around the sides and the dough sticks like crazy, you will need to add more bread flour. The dough should still sort of hold its shape, but it will look like a goo when kneading.
Make sure to knead for the entire 15-20 minutes. Then cover the bowl with a damp paper towel and let the dough rise in a warm place until doubled in size (about 2 hours).
On a floured surface, form the dough into a rectangle, about 1/2 inch thick, and one that when you roll up will fit in your loaf tin.
Line your loaf tin with parchment paper so that there are long portions of the paper hanging from two sides. Place your formed bread in and cover lightly with the hanging parchment paper and some plastic wrap.
Place in the fridge to proof for 12-18 hours. I do this overnight. The next day it should look slightly more poofy.
Take the bread out to room temperature while you preheat your oven to 330 degrees F.
Bake the bread cover with the parchment paper for 25 minutes then uncover and bake for another 20 minutes. The bread should sound hollow when you tap it and be golden brown.
Take the bread out of the loaf tin by lifting the parchment paper. Let cool on a wire rack.