Heat the oven to 350°F (175°C). Line an 8-inch square baking pan with parchment paper, leaving enough overhang to lift out the cooled brownies, then lightly grease the pan.

Whisk the melted butter and granulated sugar together in a large bowl. Add the room-temperature eggs and vanilla, then whisk until the mixture looks smooth and evenly combined.

Sift or whisk the flour, cocoa powder, and salt in a separate bowl. Stir the dry mixture into the butter mixture just until no dry streaks remain, then fold in the chocolate chips if using.

In another bowl, stir the peanut butter, confectioners' sugar, melted butter, vanilla, and optional pinch of salt until smooth. The mixture should be thick but easy to spoon.

Spread about two-thirds of the brownie batter into the prepared pan. Spoon the peanut butter mixture over the batter in several dollops, then add the remaining brownie batter in small spoonfuls.

Drag a knife or skewer through the batter using a few gentle figure-eight motions. Stop as soon as you see attractive ribbons, since excessive swirling can blend the chocolate and peanut butter layers together.

Bake for 30–35 minutes, until the edges are set and a toothpick inserted near the center comes out with moist crumbs but no wet batter. Do not wait for the toothpick to be completely clean.

Cool the brownies completely in the pan for at least 1 hour before lifting them out with the parchment. For especially clean, fudgy slices, refrigerate the cooled brownies for 30–60 minutes before cutting.