For the chocolate donuts: Preheat the oven to 375 degrees F.
Spray a 12-cavity donut pan with cooking spray and set it aside.
Whisk together the flour, granulated sugar, cocoa, salt, baking powder and baking soda in a large bowl. Whisk together the coffee, buttermilk, oil, vanilla and egg in a separate medium bowl until combined. Add the wet ingredients to the dry ingredients and mix to combine.
Transfer the batter to a piping bag. Fill each cavity with batter until it comes about three-quarters of the way up the sides of the pan.
Bake until a toothpick inserted into a donut comes out clean, about 12 minutes. Cool the donuts in the pan for 5 minutes, then remove to a rack and cool completely.
For the coffee glaze: Mix together the confectioners' sugar, coffee and milk in a bowl until smooth. If it seems too thick, add more coffee little by little.
Dip each donut halfway into the glaze, then allow excess to drip off. Sprinkle the tops with hazelnuts and sprinkles. Let set, about 30 minutes.