Preheat oven to 350 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.
Into the bowl add the peanut butter, vanilla, sugar and oil and whisk together. This should cool the batter down to be warm to touch. Whisk in the eggs until the batter is smooth. Gently stir in the flour, soda, powder and salt. Add the buttermilk and stir until smooth.
Pour half of the batter into the prepared pan and use an offset spatula to push it into the edges.
To the other half of the batter add the cocoa and milk, 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 20-30 minutes, until a cake tester turns out clean.