Add flour, cocoa powder, sugar, baking soda, and salt to a greased 8-inch square baking pan. Whisk until combined.
Make 3 depressions (or holes) in the dry ingredients – two small and one large. Pour the vinegar in one small depression, vanilla in the other small depression, and the vegetable oil in the third larger depression.
Pour the water over the pan. Mix with a wooden spoon until smooth. Make sure you get into the corners of the pan.
Bake for 35 minutes, or until a toothpick inserted comes out clean. Cool the cake completely on the rack.
For the frosting
Place vegetable shortening and peanut butter in a bowl and beat with an electric mixer until smooth and creamy.
Add two cups of powdered sugar and beat until well blended and it begins to thicken.
Add the vanilla and 1 tablespoon of water at a time.
Mix for 3 minutes or until it’s lighter and fluffy. If too thick, add a little more water and beat.