Preheat your oven to 350°F and line a muffin tin with 10 muffin liners inside. Set it aside.
In a medium size mixing bowl sift all-purpose flour, cocoa powder, baking powder, baking soda, salt, and espresso coffee powder together and set aside.
In another large mixing bowl whisk together softened butter and granulated sugar (you can use a mixer or a whisk). Add eggs, sour cream, milk, and vanilla extract, and Kahlua, whisk until smooth consistency.
Add dry ingredients into the mixture. Using a spatula, fold it together until smooth. Do not over mix.
Divide this batter between 10 muffin liners. Bake at 350°F for 18-20 minutes or until a toothpick comes out clean. When it is ready, take it out and set aside to cool off for about 10 minutes. Place the muffins on a wire rack.
For the frosting, using a hand or stand mixer, beat softened butter, powdered sugar, cocoa powder, Kahlua, and heavy cream together on a medium/high speed for about 2-3 minutes until softened.
When the cupcakes are completely cooled off, top them with the Kahlua Chocolate Frosting using a piping tip.