For cake: Bring peanut butter, water, and butter to a boil in a small saucepan. In the meantime, combine sugar, brown sugar, flour, salt, and baking soda in a large mixing bowl.
Pour boiling mixture over the dry ingredients and mix well. Add eggs, buttermilk, and vanilla extract and mix till smooth.
Pour batter into a greased sheet pan. (Mine is about 15×10″.)
Bake at 375° for 15-20 minutes or till toothpick comes out clean. Let cool for about 10 minutes, then spread with frosting.
For frosting: Bring butter, milk, and peanut butter to a boil in the same saucepan. Pour over powdered sugar in a mixing bowl. Beat till smooth. Beat in vanilla.
Pour over hot cake and spread with the back of a spoon. Sprinkle with chopped peanuts.