Preheat oven to 325 F and grease and line an 8×8 square inch pan with parchment paper.
Over medium heat in a saucepan, melt the butter. Continue to cook while the butter sputters, bubbles and foams. Once it goes silent and turns brown, immediately remove from heat and pour into a bowl, scraping up the tiny brown bits from the pan. Let cool completely.
In a large bowl, add the eggs and sugar. Beat with a hand mixer until light and fluffy - about 3-4 minutes. Add the salt and vanilla as you beat.
With the beaters on, slowly pour in the oil and the cooled brown butter. Scrape up all the brown butter bits into the bowl (those are the tasty parts!). Beat to combine then add the peanut butter and beat.
Add the flour and baking powder, and with the mixer on add the buttermilk and water. Stop beating once the batter is well mixed.
Pour half of the batter into the prepared pan. To the other half of the batter add the cocoa and a tablespoon of water, and stir to fully combine. Then pour the now chocolate batter over the peanut butter, and use the offset spatula or a butterknife to swirl the two batters.
Bake for 30-35 minutes, until a cake tester comes out clean of any wet crumbs.