Preheat your oven to 350°F (175°C) and line a muffin tin with cupcake liners.

Cream together 1/2 cup of softened butter and 1 cup of granulated sugar for 2-3 minutes until light and fluffy.

Add 2 large eggs one at a time, mixing well, then incorporate 1 teaspoon of vanilla extract, 2 tablespoons of instant espresso powder, and 1/2 cup of cooled brewed espresso.

In another bowl, whisk together 1 3/4 cups of all-purpose flour, 1/2 cup of cocoa powder, 1 teaspoon of baking powder, 1/2 teaspoon of baking soda, and 1/2 teaspoon of salt.

Gradually mix the dry ingredients into the wet mixture until just combined.

Spoon the batter into cupcake liners, filling them about 2/3 full.

Bake for 16-18 minutes; check using a toothpick for doneness.

Cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.

In a bowl, beat 1/2 cup of softened butter until creamy, then gradually add 2 cups of powdered sugar.

Stir in 2 tablespoons of instant espresso powder and 2 tablespoons of cooled brewed espresso until smooth.

Frost the cooled cupcakes generously, and optionally sprinkle with cocoa powder or chocolate shavings.