Preheat your oven to 350 degrees F. Grease the inside of a 9-inch x 13-inch baking pan and set it aside.
In a medium mixing bowl, stir together the flour, cocoa powder, and baking powder. Set aside.
In a large bowl, stir together the sugar, mayonnaise, and water. (If you use a spoon instead of a mixer, some lumps of mayo will remain, but they will incorporate into the final batter.) Add the flour mixture to the mayo mixture and mix until smooth.
Pour the cake batter into the prepared pan. Bake for 30 minutes or until a toothpick inserted into the center comes out clean.
Remove from the oven and let the cake to cool to room temperature on a wire rack.
Frosting
Once the cake has cooled, make the frosting. Beat the butter on high speed until light and fluffy, about 1 minute.
Add half the powdered sugar and all the cocoa powder to the butter and beat until smooth. Add remaining sugar and beat until combined. (The frosting will be very thick.)
Add the heavy cream a little at a time, mixing as you go, until your desired frosting consistency is reached.
Frost the top of the cooled cake and cut it into 12 slices.
Notes
You can replace the heavy cream in the frosting with milk or half-and-half if desired.