Preheat oven to 350 degrees. Line a 12-tin cupcake pan with cupcake liners.
Combine cocoa and hot coffee together, stirring until smooth; add in oil and stir; set aside.
Beat butter with a standing mixer or hand mixer until creamy and fluffy, about 2-3 minutes.
Gradually add in white and brown sugar, beating 2-3 minutes until it is light and fluffy. Add eggs, 1 at a time, beating just until the yellow disappears.
Add in chocolate/coffee mixture, and beat until just combined.
In a bowl, sift together flour, baking soda, baking powder, salt, and espresso powder.
Stir together buttermilk, vanilla extract, and sour cream (or Greek yogurt).
Alternately mix the buttermilk mixture and flour mixture with the butter batter, beginning and ending with the flour mixture. Do not overmix.
Divide batter evenly between muffin cups (the batter makes 14-16).
Bake for 17-18 minutes, or until a cake tester comes out clean. Be careful not to over-bake, as chocolate cupcakes can get very dry if over-baked.
Allow to cool.