Preheat oven to 375 degrees F. Line a 12x18 inch sheet pan with parchment paper and set aside.
In a large saucepan, combine peanut butter, water, and butter for the cake. Bring to a boil, then whisk in sugars, flour, salt, and baking soda. Add eggs, buttermilk, and vanilla until blended. Pour batter into the prepared pan and bake for 15 minutes.
Meanwhile, make the frosting by melting butter with buttermilk and peanut butter. Bring to a boil, then whisk in powdered sugar and vanilla until smooth.
Pour frosting over the warm cake and let it set. Cut into squares and serve.
Notes
Tip: Store at room temperature in an airtight container for up to 4 days.