Preheat oven to 350°F. Line a square 9x9" baking dish with a parchment paper sling or spray with baking spray.
In a large microwave-safe bowl, combine the bittersweet chocolate and butter. Microwave on high in 20-30 second bursts, stirring well between bursts of heat until melted and smooth. Whisk in cocoa powder.
4 ounces bittersweet chocolate, 3/4 cup salted butter, 1/2 cup unsweetened cocoa powder
Add granulated sugar and brown sugar, whisking well to combine. Add eggs and vanilla, beating well either by hand with a whisk or using an electric mixer.
1 cup granulated sugar, 1/2 cup light brown sugar, 3 large eggs, 2 teaspoons vanilla extract
Sprinkle the flour and salt over the brownie batter and gently stir it in with a wooden spoon or spatula. Stir in most of the chopped peanut butter cups.
3/4 cup all-purpose flour, 1/2 teaspoon salt, 1 1/2 cups chopped peanut butter cups
In a separate bowl, make the peanut butter swirl by beating the melted butter, peanut butter, powdered sugar, and vanilla together until smooth.
3 Tablespoons salted butter, 3/4 cup creamy peanut butter, 1/3 cup powdered sugar, 1 teaspoon vanilla extract
Drop about 2/3 of the brownie batter into the prepared pan by spoonfuls. Fill in gaps with spoonfuls of the peanut butter mixture. Drop remaining brownie batter on top, then swirl both together with a knife.
Bake for 30 to 35 minutes, until a toothpick inserted into the center of the brownies comes out mostly clean with only a few crumbs attached. Be sure not to overbake.
Cool completely before cutting. Store in an airtight container for up to 5 days on the counter or in the fridge.