Preheat oven to 350°F. Grease a 15x10-inch sheet pan with butter or nonstick spray.
In a medium saucepan over medium heat, combine peanut butter, water, butter, and oil. Bring to a boil, then turn off the heat.
In a large mixing bowl, whisk together self rising flour and sugar. Add the hot peanut butter mixture, and mix until smooth.
In a small bowl, whisk together eggs, buttermilk and vanilla extract. Add this mixture to the peanut butter mixture, and stir just until combined.
Pour the batter into the prepared sheet pan, spreading evenly. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs. Allow the cake to cool at least 20 minutes before adding the frosting.
For the frosting, in a medium saucepan, combine milk, peanut butter, and vanilla. Once melted and fully combined, turn off the heat and stir in powdered sugar until smooth. Spread on the slightly cooled cake. Slice and serve.