Preheat the oven to 375. Line a 12x18 sheet pan with parchment paper and set aside.
In a large saucepan, combine the peanut butter, water, and butter.
Bring to a boil, stirring constantly. Once it comes to a boil, remove from heat.
Add the white sugar, brown sugar, flour, salt, and baking soda. Mix until well combined.
Add the eggs, buttermilk, and vanilla and stir gently until blended.
Pour into the prepared pan and bake for 15 minutes.
Frosting:
While the cake is baking, prepare the frosting. In a saucepan, combine the butter, buttermilk, and peanut butter.
Bring to a boil, stirring constantly. When it comes to a boil, remove from heat and whisk in the powdered sugar and vanilla until smooth.*Make sure the powdered sugar is completely dissolved or else there will be lumps on the cake.*The frosting should be a thinnish sauce but thicker than juice. It does harden as it cools on the cake.
When the cake is completely baked, remove from the oven, pour the frosting evenly over the hot cake, then allow to cool.
Notes:
Make Ahead: This can be made early in the day and served cool, but it's best served the first day.