Line the bottom and sides of a 14 by 17-inch baking sheet (with sides) with parchment or waxed paper. Sift together the sugar, flour, cocoa, baking powder, baking soda and salt. Transfer to a mixer fitted with a whisk attachment (or use a hand mixer) and blend briefly.
In a medium bowl, whisk together the eggs, milk, oil and vanilla extract. Add to the dry ingredients and mix at low speed for 5 minutes. Gradually add the hot water, mixing at low speed just until combined. The batter will be quite thin. Pour the batter into the prepared pan. Bake until a tester inserted in the center of the cake comes out clean (a few crumbs are okay), 25 to 30 minutes. Let cool in the pan.