Preheat oven to 350 degrees. Prepare muffin tins with liners.
In a large bowl mix together sugar, flour, cocoa powder, baking powder, baking soda, and salt.
In an electric mixer combine eggs, oil, vanilla and milk. Mix until well combined. Slowly add flour mixture. Beat on medium speed for 2 minutes.
Add boiling water. Batter will be very thin.
Scoop batter into prepare muffin tins.
Bake for 20-25 minutes, until a tester comes out clean. Remove from oven, and let cool for 5 minutes before removing to a wire rack to cool completely.
Meanwhile prepare the frosting. The the bowl of an electric mixer combine all of the ingredients. Beat until light and fluffy. Add more milk or sugar if necessry.