Combine the sugar, flour, cocoa, baking powder, baking soda, and salt in a large bowl and stir with a whisk to blend.
Add the eggs, milk, molasses, oil, and vanilla and beat for 2 minutes.
Add the water and stir it into the batter by hand.
Pour the batter, which will be very thin, into a greased 9x13-inch baking pan and bake at 350 degrees for 35-45 minutes, or until a toothpick inserted in the center comes out clean.
Remove from the oven and let cool on a wire rack.
To make the frosting, combine the butter, peanut butter, and cream cheese in a large bowl and beat until fluffy.
Slowly add the confectioners' sugar, beating to form a smooth frosting.
Add the milk 1 tsp at a time until the frosting reaches the desired spreading consistency.
Frost the cake and let it sit for 30 minutes before cutting.