For starter dough, combine sticky Sweet Glutinous Rice Flour (1/2 cup), Coconut Milk (3 tablespoon), and Milk (3 tablespoon) in a microwavable bowl.
Microwave for 100 to 120 seconds, making sure to stir the dough every 30 seconds until evenly mixed and thoroughly cooked. The dough should look opaque and bouncy after microwaving. Let cool.
In a stand-mixer bowl with a dough-hook attachment, combine sticky Sweet Glutinous Rice Flour (3 1/2 cup), Milk (1/2 cup), Coconut Milk (1/2 cup), Unsalted Butter (10 tablespoon), Granulated Sugar (1/2 cup), Large Egg (2), and Baking Powder (2 teaspoon).
Incorporate the cooled starter dough into the mixture and knead on low. Gradually increase the speed to medium and knead until the starter dough and mixture are perfectly blended.
Transfer the dough to a surface dusted with sticky rice and knead while slowly incorporating sticky Sweet Glutinous Rice Flour (1 cup). Once the dough is smooth and does not stick to your hands, sprinkle some flour on it and roll it until it is 3/4 inches (2 centimeters) thick.
With a floured cutter or a round glass, cut the rolled dough into doughnuts. Use a chopstick to make the holes by sticking it in the center and swirling until the hole is 1 to 2 inches wide. Gather the scraps and recombine them into the dough for more doughnuts.
Pour Sunflower Oil (to taste) into a deep frying pan until 1 1/2 inches (4 centimeters) deep. On medium high, bring oil to 330 degrees F (165 degrees C), and then turn the heat down to medium-low. Gently place a few doughnuts into the oil, ensuring they don't stick together.
The doughnuts will sink to the bottom for the first 30 seconds, then float to the top. Fry for a few minutes on each side until the doughnuts are risen and brown.
Transfer to a cooling rack or paper towel to drain the excess oil. Regularly check the temperature of the oil to make sure it doesn't get too hot.
For glaze, combine Unsalted Butter (5 tablespoon) with Powdered Confectioners Sugar (2 cup) and Vanilla Extract (1 teaspoon). Stir in Water (4 tablespoon) to bring to a desired glaze consistency. Add Matcha Powder (1 1/2 tablespoon) and whisk until smooth.
Dip one side of the doughnuts into the glaze.
Sprinkle the glazed side with Unsweetened Coconut Flakes (1/2 cup).
Serve within a few hours and enjoy!