I've seen it by various other names, we always called it crazy. The only change I made from the original recipe I used as a child is that I use coconut oil in place of vegetable oil, and I cut the amount of soda since I now live at high altitude.
The icing recipe is the same one my grandmother used. It's very much like old fashioned fudge (back before marshmallow fudge took over). I cook it a little longer than I used to, again, because of the altitude. My mother used to beat it over a pan of ice water to thicken it to frosting consistency, but I pour it on warm, so that some of the icing will soak into the cake before it cools.
Crazy Chocolate Cake
1 cup sugar
1 1/2 cup flour
3 tablespoons cocoa
1 teaspoon baking soda
1/2 teaspoon salt
1 tablespoon vinegar
6 tablespoons melted coconut oil
1 cup water
Blend dry ingredients in a 9x9 inch square baking pan. Make a well in the center and add the remaining ingredients. Blend with a fork.
Bake at 350 degrees for 30 to 40 minutes
Chocolate Icing
1 cup sugar
1/2 cup water
3 tablespoons cocoa
1 teaspoon vanilla
2 tablespoons butter
Mix sugar, water and cocoa in a medium saucepan (it will bubble up quite high when it boils).
Bring to a boil and cook without stirring for 5-7 minutes. Remove from heat and add butter and vanilla. Beat until thick.