01 - Preheat oven to 350°F. Line a 12-cup muffin tin with cupcake liners.
02 - Sift together flour, cocoa powder, sugar, baking powder, baking soda, and salt in a large bowl.
03 - Whisk eggs, milk, vegetable oil, and vanilla extract in a separate bowl.
04 - Add wet ingredients to dry ingredients and mix until just combined.
05 - Gradually incorporate hot water and stir until batter is smooth and thin.
06 - Divide batter evenly among cupcake liners, filling each about two-thirds full. Bake 16 to 18 minutes until a toothpick inserted in the center comes out clean.
07 - Allow cupcakes to cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.
08 - Beat softened butter until creamy. Sift in powdered sugar and cocoa powder, then add milk, vanilla, and salt. Beat until fluffy and spreadable, adding milk if needed.
09 - Once cupcakes have fully cooled, frost generously with prepared frosting using a piping bag or spatula.