Preheat your oven to 350°F. Line a 12 count cupcake tin with paper liners, and set aside. Make the chocolate espresso cupcakes: In a medium sized bowl or cup, whisk together espresso powder and water until the espresso is dissolved. Set aside to cool slightly while you prep the rest of the batter.
In a medium bowl, combine flour, cocoa powder, baking powder, baking soda, and salt. Whisk to combine and set aside.
In a large bowl, combine butter and sugar. Using an electric mixer fitted with the beater attachment or a wooden spoon by hand, cream together the butter and sugar until the sugar is fully dissolved. This will take about 1 minute on medium speed or 2 to 3 minutes by hand. It doesn't need to be fluffy, and the mixture will still be grainy. Add in your egg and vanilla extract, and whisk to combine. Alternate adding dry ingredients and wet ingredients to the butter/sugar mix. Start by whisking in about 1/3 of the dry ingredients, followed by all of your buttermilk. The mixture may look a bit clumpy and separated at this point, but that's normal! Whisk in another 1/3 of the dry ingredients, followed by the coffee. Finish off by mixing in the final 1/3 of your dry ingredients until just combined.
Portion your batter into your prepared cupcake tin, filling each cup no more than about 2/3 of the way full. You may need to do two batches depending on the size of your paper liners. Bake the cupcakes in the center of your preheated 350°F oven for 15 to 20 minutes, or until a toothpick inserted into the center comes out clean.
Cool the baked cupcakes in the tin for about 10 minutes, then transfer onto a wire rack and set aside to cool completely to room temperature before frosting.
Make the espresso buttercream: In a small bowl, whisk together your espresso powder and boiling water until the espresso is dissolved. Set aside to cool completely to room temperature before using.
In a large bowl, combine butter and powdered sugar. Using an electric mixer fitted with the beater or whisk attachment, cream together until light and fluffy (about 2 to 3 minutes on medium speed). You can do this by hand, but it's quite a workout!
Add your cooled espresso/water mix and vanilla to the butter mixture. Beat together for another 1 to 2 minutes, or until light and fluffy. If your frosting is too stiff, gradually add more room temperature water, 1 tablespoon at a time, until it reaches your desired consistency.
Frost your cooled cupcakes, and serve!