Whisk the glutinous rice flour, rice flour, sugar, and salt in a mixing bowl. Stir the ube extract into the warm water, pour it in, and mix, then knead for 3 minutes until the dough is smooth and soft like play dough. If the edges crack, knead in extra water 1 tsp at a time. Cover with a damp towel and rest for 10 minutes.
While the dough rests, pour 5 cm / 2 inches of water into a 28 cm / 11-inch wok or pot and bring it to a boil. Line both tiers of the 26 cm / 10-inch bamboo steamer with banana leaf or perforated parchment and brush lightly with oil.
Oil your hands and divide the dough into 12 portions of about 45 g each. Roll each into a log about 8 cm / 3 inches long and 2.5 cm / 1 inch thick. Set 6 logs on each tier in two rows of three, 2 cm / 3/4 inch apart.
Stack the tiers over the boiling water and wrap the lid in a clean kitchen towel. Steam over medium-high heat for 18 minutes, until the logs are deep purple, glossy, and spring back when pressed.
Move the hot logs to a platter and brush each with the softened butter so it melts into the surface. Sprinkle with muscovado sugar and top with the coconut. Serve within 15 minutes.