Pre-heat the oven to 375 and spray a 6 well donut pan with unflavored cooking spray. In a small pot, bring the 1/4 cup of water to a boil. Stir in the espresso powder and let it dissolve in while you keep stirring for a minute. Take it off the heat and let it cool. While it cools, whisk the flour, brown sugar, baking powder, cinnamon and salt together in a bowl for the dry ingredients. Get out a stand mixer and fit it with the paddle attachment. Combine the cooled espresso (keep the pot out), vegetable oil, vanilla, and egg in its bowl. Mix them together until smooth on low. Then slowly pour in the dry ingredients until you have a very soft batter. 

Scoop the batter into a piping bag or a ziplock bag and cut the tip. Pipe the batter evenly among the 6 donut wells so that they are all about a little over halfway full. Bake them for 10-12 minutes, until puffy and springy. While they bake, make the easy glaze. Bring the 2 tablespoons of water to a low boil and dissolve the espresso in it just like you did before. Pour it into the powdered sugar and stir it together. Pour in a dash or two of water to thin it out and make it an easily pourable glaze. If you find it got too watery, just add a little more sugar. Let the donuts cool for 2-3 minutes once they are done and turn them out onto a rack to cool some more. Submerge the top half of each donut in the glaze and transfer them to a plate to top side up to harden. Serve immediately and enjoy! They also keep for a day or two in a sealed container.