Preheat oven to 350 degrees F. Spray a cupcake pan with cooking spray and set aside. Or, line with cupcake liners.
Mix the non-dairy milk and vinegar and set aside for 10 minutes to make a vegan buttermilk.
Whisk together the flour, cocoa powder, baking powder, baking soda and salt in a medium bowl and set aside.
In a small bowl or cup, dissolve the espresso powder with hot water and set aside.
Place the sugar, apple sauce, peanut butter, oil, and vanilla in a large bowl and whisk by hand or with an electric mixer. Add in the buttermilk mixture of milk and vinegar and the flour and cocoa mix and continue to mix until smooth. Whisk in the espresso and mix together until smooth, the batter will be on the thin side.
Divide into the prepared cupcake pan, filling a scant 3/4 way full. Bake for 20 minutes, or until a toothpick comes out clean. Remove and let cool while you make the frosting.
In the bowl of a stand mixer or an electric hand mixer, beat together the softened butter and peanut butter until smooth. Add the powdered sugar and vanilla. Whisk until smooth and fluffy. If the frosting seems dry, add more non-dairy milk, a tablespoon at a time. If it is too wet, add powdered sugar to thicken.
Frost the cupcakes and enjoy. I use a cupcake corer to put some of the frosting into the center of the cupcake, like a Hostess-style cupcake!
Notes
* I use Earth Balance, which is salted. If using an unsalted butter, then add a pinch of salt to the frosting.**For fun, I drizzle on melted chocolate and finely chopped peanuts after frosting.