Add sugar to a mixing bowl of a stand mixer. Sift the flour, cocoa powder, baking soda, baking powder, salt into the sugar bowl. Whisk, and set aside.
In a small bowl, beat the eggs, oil, milk and vanilla. Add this mixture to the sugar/flour mixture of the stand mixer bowl. Using the paddle attachment, mix the ingredients on low just until incorporated, about 30 seconds.
With mixer off, pour in the espresso and boiling water. Mix by hand until all ingredients are incorporated. A few lumps are ok. The batter will be runny. Let batter rest for 5 minutes.
Line muffin pan with cupcake cups. Fill each cup to 3/4 full. Use a #20 ice cream scoop to make portioning a snap! One scoop per cup. Or, fill each cup 3/4 full, about 3 Tbs. Bake cupcakes for 25 minutes (but start checking for doneness at 22 minutes using the toothpick test).
Once out of the oven cool cupcakes, in pan, on a cooling rack for 10 minutes. Then remove from pan and let cool completely before icing.
For The Icing
In a stand mixer, using a paddle attachment, cream the butter until light and fluffy, about 5 minutes.
While the butter is creaming, sift together the powder sugar and cocoa powder. Once the butter is creamed, add the sifted cocoa and sugar alternatively first with all of the vanilla extract, then with 2-3 TBS of milk at a time reserving the last two TBS for consistency adjustment. The icing should be spreadable, not too stiff or loose.
Once the cupcakes are cool, pipe the icing on the cupcakes. Store in a covered container at room temperature for up to three days.
These cupcakes are very moist and you'll find the tops are sticky. *Unbleached white flour may also be used instead of Whole Wheat White, but the texture will be slightly different. **Omit the water and use 1 C of very hot strong coffee for a BIG bold espresso flavored cupcake! Adapted from Hershey's