In a small microwavable bowl, mix together the sticky rice flour and whole milk. Heat it in a microwave on high for 30 seconds. Give everything another quick stir, and heat for another 15-20 seconds, until the dough is cooked through. It will look opaque and feel firm, but springy to the touch. Set aside to cool for several minutes.
To make the main donut dough
Using a stand mixer with the dough hook on low speed, mix together the sticky rice flour, whole milk, unsalted butter, granulated sugar, egg, baking powder, Matcha powder and starter dough, until everything is well mixed and the starter dough is completely incorporated. The dough will be wet and sticky, but it shouldn't "glue" itself to your hands when you touch it. If needed, add in more milk by the teaspoon (I added in 2 more teaspoons).
Dust a work surface with sticky rice flour, and transfer the dough onto the surface. Cut the dough into four pieces. Roll each piece into a long tube, about ½-inch to 1-inch in diameter, depending on how large you want the mochi donut holes to be. I used a variety of sizes between ½-inch to 1-inch. Cut each tube into about 15 pieces equal pieces.
Using the palms of your hands, roll each piece into a ball, and place on a plate that is lightly dusted with sticky rice flour. You should get roughly 60 donut holes.
Heat oil in a deep fryer to 330°F/165°C. Without crowding the pot, carefully place in several donut holes. The donut holes will immediately sink to the bottom for the first 30 seconds, then they will flat back up. Fry, rotating as needed, until the donut holes are puffed up and lightly golden brown. Transfer to a cooling rack to drain. Repeat with the remaining donut holes, making sure that the oil stays at a consistent temperature. (See notes below for a quick tip.)
In a small bowl, make the dusting sugar by mixing together the powdered sugar with the Matcha powder. Once the donut holes have cooled, sift the dusting powder over all the donut holes, rotating if desired.
This recipe is adapted from Lady and Pups. Tip for quickly transferring the donut holes into the deep fryer: Place about 6 donut holes on a small sheet of parchment paper. Transfer the entire sheet of parchment paper, with the donut holes on top, into the deep fryer. Carefully remove the parchment paper using tongs once the donuts have floated up.