Adjust oven rack to lowest position and preheat oven to 350 degrees F. Spray a 9x13-inch pan with non-stick cooking spray, then line with parchment paper, leaving about a one-inch overhang on the sides.
Prepare the Peanut Butter Filling: Melt the peanut butter and unsalted butter together in a medium bowl in the microwave until completely melted and smooth, 1 to 2 minutes, stirring occasionally. Whisk in the vanilla extract, then gradually whisk in the powdered sugar until completely smooth. Set aside while you prepare the brownie batter.
Prepare the Brownies: Whisk the cocoa powder and boiling water together in a large bowl until smooth. Add the unsweetened chocolate and whisk until the chocolate is melted. Whisk in the melted butter and oil (the mixture may look curdled at this point, that’s okay!). Add the eggs, yolks, and vanilla extract, and whisk until smooth and homogeneous. Whisk in the sugar until fully incorporated. Add the flour and salt and mix with a rubber spatula until combined. Fold in the chocolate chips, if using.
Pour half of the batter into the prepared pan, spreading into an even layer.
Turn the peanut butter filling out onto a clean work surface and press into a rough 9x13-inch rectangle. Transfer that filling using your fingers or a thin metal spatula onto the brownie batter in the pan. You can do this in sections and it doesn’t have to be perfect. Pour the remaining batter over the peanut butter filling and gently spread into an even layer.
Bake until a toothpick inserted halfway between the edge and center comes out with just a few moist crumbs attached, 28 to 35 minutes. Transfer the pan to a wire rack and cool for 1½ hours.
Using the parchment overhang, lift the brownies from the pan. Place the brownies on the wire rack and cool completely, about 1 additional hour. Cut into squares and serve. The brownies can be stored in an airtight container at room temperature for about 4 days.
Cocoa Powder: The brownies call for Dutch-process cocoa powder, which imparts a wonderfully rich flavor and I highly recommend, but the recipe will still work if you substitute regular unsweetened cocoa powder.
Chocolate: For unsweetened chocolate, I typically turn to Ghiradelli, Baker's, or Guittard.
Peanut Butter: For best results, use a "processed" style peanut butter such as Jif or Skippy and avoid natural-style peanut butter that separates and needs to be stirred.
Substitute Nut Butters: You can replace the peanut butter with other similarly processed nut butter, such as Barney Butter almond butter, Sunbutter, or processed cashew butter.
Mix-In Ideas: The brownie recipe calls for optional chocolate chips in the batter, but you could swap in things like chopped nuts, peanut butter chips, Reese's Pieces, or chopped peanut butter cups.
Make-Ahead: You could prepare the peanut butter filling, press it out and place it in the refrigerator up to a day before assembling and baking the brownies.
How to Store the Brownies: The brownies can be kept in an airtight container at room temperature for up to 4 days.
Freezing Instructions: You can freeze the brownies by wrapping them individually in plastic wrap, then placing in an airtight container for up to 3 months. Thaw at room temperature for about 45 minutes before enjoying.