With the rack in the middle position, preheat the oven to 180 °C (350 °F). Line 18 muffin cups with paper or silicone liners. Set aside.
In a bowl, combine the sugar, flour, cocoa powder, baking powder, and salt. Set aside.
In a large bowl, combine the eggs, water, oil, vinegar, and vanilla with a whisk. Add the dry ingredients and stir until the batter is smooth.
With a 45 ml (3 tablespoons) ice cream scoop, spoon the batter into the cups. Bake for about 20 minutes or until a toothpick inserted in the centre of a cupcake comes out clean. Let cool on a wire rack.
In a bowl, beat together all the ingredients with an electric mixer until the frosting is smooth.
With a spreading knife or pastry bag fitted with a plain or fluted tip, frost the cooled cupcakes.