Preheat the oven to 350°F. Lightly oil a 6 cavity doughnut pan.
In a medium mixing bowl, stir together the flour, sugar, matcha, baking powder, and salt. In a separate bowl or liquid measuring cup, stir together the milk, coconut oil, and vanilla. Add the milk mixture to the flour mixture and stir just until fully mixed and a thick batter forms.
Pipe or spoon the batter into the doughnut cavities. Place the pan into the oven and bake for 10 to 12 minutes, until the tops spring back when lightly touched.
Remove the pan from the oven and transfer to a cooling rack to cool completely.