Preheat oven to 350 degrees F. Lightly grease a donut pan.
In a medium bowl, whisk together the dry ingredients.
In a small saucepan, melt butter until it starts crackling. Whisk constantly until butter begins to brown and brown bits are visible. Remove from heat and pour into a small bowl. Let cool for a few minutes.
In a large measuring cup (or small bowl) whisk together buttermilk, egg, vanilla extract and two tablespoons of brown butter.
Add the wet ingredients to the dry ingredients all at once and stir until combined. Mix only until all the flour bits are gone. Do not overmix.
Spoon batter into prepared pan. Fill each donut ¾ of the way and smooth.
Bake for 8-10 minutes. Remove from oven and let cool for a few minutes before inverting onto a cooling rack. Let cool completely before glazing.
To make the glaze:
Whisk together all the ingredients in a medium bowl. Add a tablespoon of milk if necessary to have a thick but pourable glaze.
Dip cooled donuts top-side-down into chocolate glaze. Sprinkle with toppings. Allow glaze to set for 30 minutes before serving or stacking.