Spray donut pans with nonstick spray and preheat oven to 350 degrees F.
In a large mixing bowl, whisk mochiko, baking powder, salt, sugar, brown sugar, and cocoa powder.
In a separate mixing bowl, beat eggs, coconut milk, evaporated milk, and melted butter until combined.
Add dry ingredients to wet ingredients and mix well.
Pipe batter into donut pans, filling them all the way to the top. Leftover batter can be covered with towel or plastic wrap and left at room temperature until the first batch is done baking.
Bake donuts for 20-30 minutes or until cooked all the way through. You can tell it's done when the edges pull away slightly from the pan, the top feels springy to the touch, and a toothpick inserted comes out clean.
Allow donuts to cool to room temperature.
For the glaze, heat matcha and milk until steaming. This can be done on stovetop or in the microwave, but be careful not to overheat.
Whisk matcha and milk until well combined and pour over the white chocolate. Stir until chocolate is melted and everything is combined.
Dip cooled donuts in the white chocolate glaze and top with sprinkles, if using.