Preheat oven to 325F/162C degrees. Lightly grease an 8 donut baking pan and set aside.
In a medium bowl, add the flour, cacao powder, baking powder, and salt. Mix until thoroughly combined using a wire whisk. Set aside.
In a large bowl, add the egg and lightly beat with the wire whisk. Add the sugar and beat for about 2 minutes, then mix in the Nutella, milk, brewed coffee, butter, and vanilla extract. Gradually dry bowl of dry ingredients and mix well. Fill each donut cup ¾ full and place in the preheated oven to bake for 10 minutes, or until the donut springs back when touched.
All cooked donuts to cool slightly in the pan, about 3 minutes, before removing them to a wire cooling rack.
Make the glaze by combining the powdered sugar, brewed coffee, and vanilla extract in a small bowl. Mix well until all sugar lumps disappear. Set aside.
Once donuts have cooled completely, dip each one in the coffee glaze, then return to the wire rack to set. Serve immediately or store in an air-tight covered container.
Leftovers will stay fresh for 2-3 days in an air-tight covered container.