• Preheat oven to 350 degrees F.
• Line a 9x13 inch pan with parchment paper.
• With an electric mixer, cream together softened butter, brown sugar, white sugar, and peanut butter until smooth. Mix in egg, yolk, milk and vanilla until smooth. Add the baking soda and salt and mix by hand or with the mixer until they disappear, then add the flour and mix on low or by hand until blended. Add peanut butter chips if using. Set the dough aside.
• Prepare Brownie Batter: Melt butter in a 3 quart saucepan. Remove pan from heat and add oil and sugar. Return to heat for about 30 seconds to melt the sugar a bit, then remove from heat. Now add the cocoa powder and stir until fully blended. Let cool slightly before adding eggs (about 5 to 7 minutes).
• Crack the cold egg and egg white into a small bowl and mix with a fork, then gradually add them to the warm chocolate mixture, beating with a scraper until smooth and shiny. Add the vanilla.
• Mix together the flour, baking powder and salt, then add to the chocolate mixture. Beat by hand with a heavy duty scraper until well mixed. The brownie batter should be dark and shiny.
• Spoon about half of the peanut butter cookie dough over the bottom of the pan and press down lightly. You don't have to cover the entire pan bottom.
• Spread the brownie batter in the pan, covering the peanut butter dough. Sprinkle chocolate chips over it.
• Drop spoonfuls of remaining peanut butter dough over the brownie batter, then gently spread, doing your best to cover the brownie batter. The cookie dough should be such that you can spoon it and kind of stretch it with your fingers. Sprinkle more peanut butter and chocolate chips over the top if desired.
• For the 9x13 inch pan version, bake at 350 degrees F for 27-32 minutes or until toothpick when inserted comes out clean and cookie dough is lightly browned. If you have an instant read thermometer, insert it in the center. Temperature should top out around 200F.
• These take a while to cool. Let cool at room temperature until the pan is no longer hot, then transfer to a freezer or the refrigerator to speed things up. When cold, drizzle with melted chocolate mixture.

Half Batch 8-Inch Square Pan Version

• For a half batch, halve all the ingredients, assemble in an 8-inch square pan. Instead of baking at 350 degrees F, bake at 325F for about 35 minutes or until brownies top out at about 200 degrees F.