Preheat oven to 375°F and grease a donut pan.
In a large bowl, whisk together flour, cocoa powder, baking soda, salt, and brown sugar.
Add buttermilk, egg, vanilla, and vegetable oil. Mix until just combined.
Stir in hot water until batter is smooth.
Spoon the batter into the donut pan, filling each cavity about 2/3 full.
Bake for 8-10 minutes or until donuts spring back when lightly pressed.
Let cool for 5 minutes in the pan, then transfer to a wire rack.
For the glaze, whisk together powdered sugar, milk, and vanilla extract until smooth.
Dip cooled donuts into the glaze and place back on the rack to set.