Preheat the oven to 375 degrees. Spray a doughnut pan with non-stick baking spray and set aside.
In a large mixing bowl, whisk together the flour, sugar, cocoa powder, baking powder, baking soda, espresso powder and salt. In a small bowl, beat together the egg, yogurt, milk, butter and vanilla.
Stir the wet ingredients into the dry ingredients until combined. Spoon the batter into the wells of the doughnut pan, filling each about ¾ full.
Bake the doughnuts for 9-10 minutes, or until the tops spring back when you touch them.
Allow the doughnuts to cool in the pan for about 5 minutes, then remove them from the pan and set them on a cooling rack to finish cooling completely.
To make the glaze, whisk all of the ingredients together in a small bowl. Dip the cooled doughnuts fully into the glaze to coat them completely. Allow them to rest on a wire rack until set.
Recipe by Exploring Food & Drink in D.C. at https://www.epicureandc.com/chocolate-espresso-glazed-doughnuts/