Preheat your oven to 350°F (175°C). Grease and flour a large sheet pan (approximately 18x13 inches).

In a large mixing bowl, combine the flour, sugar, baking soda, salt, and cocoa powder. Whisk until well blended.

In a saucepan, melt the butter and water together over medium heat, stirring until the butter is completely melted. Remove from heat and let cool slightly.

Add the melted butter and water mixture to the dry ingredients, mixing until just combined.

In a separate bowl, whisk together the eggs, buttermilk, and vanilla extract. Add this mixture to the batter and stir until smooth.

Pour the batter into the prepared sheet pan and spread evenly. Bake for 20-25 minutes, or until a toothpick inserted in the center comes out clean.

While the cake is baking, prepare the peanut butter frosting. In a mixing bowl, beat the softened butter and peanut butter together until creamy. Gradually add the powdered sugar, alternating with the milk, and mix until smooth. Stir in the vanilla extract.

Once the cake is done baking, remove it from the oven and let it cool in the pan for about 10 minutes. Spread the peanut butter frosting over the warm cake.

Let the cake cool completely before slicing into squares.