Pre-heat oven to 350F. Line a 12-cupcake pan with cupcake liners or grease it with butter and flour.
Sift flour, cocoa powder, sugar, baking soda, baking powder, espresso powder, and salt together in a large bowl.
In another bowl, mix coffee, vinegar, Kahlua and oil. Pour dry mixture over wet ingredients. Whisk briefly, until incorporated. Be careful not to overmix. As soon as you see no more streaks of dry mixture, stop whisking.
Distribute batter evenly in cupcake pans.
Bake for 15-20 minutes.
Remove and let it cool.
Coffee Cream Cheese Frosting
Start by sifting the powdered sugar. Set it aside.
Now, cream the softened cream cheese and butter together in the bowl of an electric mixer, for about 2 minutes, until light and fluffy.
Add Kahlua, or vanilla extract. Mix to combine.
With the mixer off, add powdered sugar mixture to the bowl.
Turn mixer on low to incorporate the powdered sugar with the cream cheese and butter.
Once you see no streaks of dry powdered sugar, cream mixture on medium high for one minute.
At the very end, add espresso powder and stir to combine.
This frosting will store well in the fridge for up to 5 days, covered.
Make sure to always leave your frosting covered. Cover the bowl with a lid or plastic wrap, because otherwise, the surface will dry out and get hard.