In a medium bowl, whisk together the coconut oil and sugar. Add the egg and whisk to combine. Add the baking powder, baking soda, matcha powder, nutmeg, salt, and vanilla and whisk to combine.
Alternately add the flour and the milk, beginning with the flour, until thoroughly combined. The batter will be thick, and a spatula drawn through the batter should leave an indentation.
Spoon the batter into the doughnut pan (it will be thick and sticky). Bake for 10 minutes. Remove from the oven and let sit for 5 to 10 minutes before removing from the pan. Remove from the pan and place on a wire rack to continue cooling.
Make your desired decorating option:
Matcha Glaze: In a small doughnut-sized bowl, whisk together the powdered sugar and matcha powder, then whisk in the almond milk until smooth. Dip each doughnut in the glaze and let the excess glaze drip off.
Matcha Cane Sugar: In a small doughnut-sized bowl, mix the cane sugar and matcha powder. Add the melted coconut oil to a separate bowl and dip both sides of each doughnut first into the coconut oil, and then into the sugar mixture. The coconut oil helps the sugar adhere and it also produces the most fried-doughnut-like taste.
Matcha Powdered Sugar: In a small doughnut-sized bowl, mix together the powdered sugar and matcha powder. Dip both sides of each doughnut into the sugar, tapping off any excess.