Combine 1 cup of ube paste with softened butter. Set aside until ready to fill dough.
Grease a 10-inch round cake pan (or 9-inch) and line bottom with parchment paper. Set aside.
Punch dough risen dough and transfer to a lightly floured work surface. Roll dough out to a 21 x 12-inch rectangle. Evenly spread ube paste over rolled dough, leaving an ½-inch border along the sides.
Starting at the longer end, roll dough into a log. Pinch seams together and place log seam-side down on work surface. Use a sharp knife to slice log in half lengthwise, leaving about 1-inch uncut on top.
Carefully twist the two pieces to allow the filling to face up. Gently braid the two pieces together. Take the two ends and pinch together to form a circle. Place in prepared cake pan. Cover and allow dough to rest at room temperature for 30 minutes until dough has puffed up.
Preheat oven to 350° F. Remove cover and bake dough for 40 minutes. If dough is browning too fast, cover with foil to prevent bread from burning. Rotate pan and bake for another 15-20 minutes, until internal temperature of dough registers at least 185° F on a kitchen thermometer. Allow bread to remain in pan for 15 minutes before unmolding. Cool bread on wire rack. Serve bread warm, toasted, or at room temperature.