In a medium bowl, sift together flour, cocoa powder, espresso powder, baking soda, and salt. Keep aside.
In another bowl, beat together the butter and sugar on medium speed until light and fluffy, about 2-3 minutes.
Scrape down the sides and bottom of the bowl as necessary.
On medium speed, beat in eggs, one at a time, beating well after each addition.
Stir in the vanilla extract and beat until combined.
With the mixer on low speed, add half of the dry ingredients and beat just until combined. Then beat in milk, followed by the other half of the dry ingredients, beating slowly until combined.
Add hot water and beat just until combined.
Do not over mix—the less you mix, the lighter the cake will be. The batter should be liquid.
Divide batter evenly between cups, filling them about ¾ full.
Bake for 15-20 minutes, or until a toothpick inserted into the center comes out clean or with just a few moist crumbs.
Allow cupcakes to sit for 10 minutes, then remove from pan and allow to cool completely on a wire rack.