Preheat your oven to 350°F (175°C) and line a muffin tin with cupcake liners.
In a large mixing bowl, whisk together the granulated sugar, brown sugar, and melted butter until combined.
Add the eggs, one at a time, mixing well after each addition. Then, stir in the vanilla extract and salt.
In a separate bowl, sift together the all-purpose flour, cocoa powder, and instant espresso powder.
Gradually add the dry ingredients to the wet mixture, mixing until just combined. Do not overmix.
Dissolve the instant espresso powder in hot water and then fold it into the batter until fully incorporated.
Divide the batter evenly among the prepared cupcake liners, filling each about two-thirds full.
Bake in the preheated oven for 18-20 minutes or until a toothpick inserted into the center comes out with a few moist crumbs. Allow to cool in the pan for 5 minutes, then transfer to a cooling rack.
While the cupcakes cool, prepare the coffee buttercream frosting. In a mixing bowl, beat the softened butter until creamy.
Gradually mix in the powdered sugar and beat until fluffy. Add the brewed coffee, vanilla extract, and optional instant espresso powder, and mix until smooth and creamy.
Once the cupcakes are completely cooled, frost them generously with the coffee buttercream using a piping bag or a knife.
Serve and enjoy your espresso brownie cupcakes with coffee buttercream!