First, whisk flour and milk in a saucepan. Cook over low heat until thick. Cool completely.
Next, mix bread flour, sugar, yeast, and salt in a bowl.
Then, add warm milk, vegan butter, and tangzhong. Knead until smooth and elastic.
After that, cover and let the dough rise until doubled, about 1 hour.
Meanwhile, mix ube halaya with milk until spreadable.
Then, roll the dough into a rectangle. Spread ube evenly on top.
Next, roll tightly into a log. Cut lengthwise to expose the swirl.
Afterward, twist gently and place in a greased loaf pan.
Finally, let rise again for 30 minutes. Bake at 350°F (175°C) for 30–35 minutes until golden.