Preheat the oven to 350°F (175°C) and grease a 9x13-inch baking pan.
In a large bowl, whisk together flour, sugar, baking soda, and salt.
In a saucepan, combine butter, water, and peanut butter. Heat until melted and smooth.
Pour the hot mixture into the dry ingredients and mix well.
Add eggs, buttermilk, and vanilla. Mix until smooth.
Pour the batter into the prepared pan and bake for 25-30 minutes, or until a toothpick comes out clean.