Preheat oven to 350°F and place the oven rack in the middle of the oven.
Generously grease the sides and top of two non-stick donut pans with soft butter. (Alternatively, you can bake these as muffins - the batter for 1 muffin is the same amount as for 1 donut).
In a medium bowl, whisk together the sweet rice flour, dark brown sugar, cocoa powder or black sesame powder, baking powder, and salt.
In a large mixing bowl, whisk together the melted butter, coconut milk, eggs, and vanilla extract. Pour in the melted cooled chocolate and mix until smooth.
Add the dry ingredients to the wet ingredients and mix until completely combined.
Divide the batter among the 12 donut cavities of the prepared donut pans, filling each one all the way to the top edge.
Bake 32-35 minutes until the top is set and the donut gently springs back when poked with a finger. It might not spring back as much as a muffin: do not bake any longer than 35 minutes. The donuts crisp up as they cool and if you continue baking them, they'll get ROCK HARD on the outside. If you like your donuts a little gooey, bake 30-31 minutes.
Let cool 10 minutes in the pan, then transfer to a wire rack to cool completely before glazing.
Prepare the glaze just before you're ready to glaze the donuts because it will firm up as it sits.