Preheat the oven to 350°F / 175°C. Line a 12-cup muffin pan with paper liners.
Whisk ¾ cup of all-purpose flour, ½ cup of natural unsweetened cocoa powder, 1 teaspoon of espresso powder, ¾ teaspoon of baking powder, ½ teaspoon of baking soda, and ¼ teaspoon of salt.
In a large bowl, whisk 2 large eggs, ½ cup of granulated sugar, ½ cup of packed light brown sugar, ⅓ cup of vegetable oil, and 2 teaspoons of vanilla extract until completely smooth.
Stir in the dry ingredients in two halves, alternating with ½ cup of buttermilk, just until combined.
Fill the liners halfway. Bake for 18-21 minutes, until a toothpick inserted into the center comes out clean. Cool completely.
For the frosting, beat 1 cup of softened unsalted butter on medium speed until creamy. Add 3½ cups of icing sugar, ½ cup of unsweetened cocoa powder, 3 tablespoons of heavy cream, and ⅛ teaspoon of salt.
Beat on low speed, then on high until smooth. Frost the cooled cupcakes.