Preheat oven to 350 degrees F (177 degrees C).
Prep donut pan by greasing it with oil or butter. I used a donut pan with donut molds that are 3 inches in diameter. Set aside.
Brown your butter. Heat butter over medium heat until it melts. Lower the heat to low and cook until brown bits start to appear. Pour into a large bowl. Let it cool for 1-2 minutes.
Add the brown sugar and egg. Mix until incorporated.
Add the coconut milk, lemon juice, lemon zest, vanilla extract, and salt. Mix until well incorporated.
Add the sweet rice flour and baking powder. Mix until incorporated.
Lastly, add the blueberries and fold them into the batter.
Spoon the dough into a pastry bag or Ziploc bag. Pipe the donuts into the prepared donut pans.
Bake for 12-14 minutes until a toothpick comes out clean.
Let donuts cool in the donut pan for 10 minutes. Transfer to a cooling rack to cool completely.
While the donuts are cooling, combine all the ingredients for the glaze. Mix and set aside. If the glaze is not thick enough for you, add more powdered sugar.
Dip the donuts into the glaze and enjoy!