Generously grease your donut baking tin and preheat oven to 350°F. It's very important to grease your tin well to avoid sticking.
In a medium mixing bowl, whisk together the flour, baking powder, baking soda, salt, and ground cinnamon
In a separate bowl, mix together the egg and brown sugar. Then, add the milk, sourdough discard, vegetable oil, and vanilla extract and mix to combine. Add the wet ingredients to the dry and mix until just combined, being careful not to overmix.
In a small bowl, toss together the blueberries and 2 tsp of flour. This prevents the blueberries from sinking to the bottom of the batter.
Pour or spoon the batter into the donut tins, filling about 1/3 of the way. Place 5 - 6 blueberries into each donut mold. Pour more batter into each tin, covering the blueberries and filling the mold 2/3 - 3/4 of the way full.
Bake for 9 - 10 minutes until a toothpick comes out clean. A little blueberry juice is okay. Remove the donuts and set aside to cool.
While the donuts cool, prepare the glaze. In a small bowl, whisk together the powdered sugar, vanilla extract, and 1 tbsp of milk. If the glaze is too thick, add a little more milk.
Once the donuts are cool, remove from the pan and dip into the glaze. Donuts are best enjoyed immediately.