Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Stir brownie mix, vegetable oil, 2 eggs, and water in a large mixing bowl until smoothly combined and gently mix the chopped peanut butter cups into the batter.
Beat peanut butter, sugar, butter, flour, vanilla extract, and 1 egg together in a bowl with an electric mixer until thoroughly combined. Spread half the brownie batter into the bottom of the prepared baking dish and top with 1/4-cup dollops of peanut butter mixture in an even pattern. Pour remaining brownie batter between the dollops. Use a knife to lightly swirl the peanut butter mixture into the brownie batter; do not overmix.
Bake in the preheated oven until a toothpick inserted into the center of the brownies comes out with moist crumbs, 30 to 40 minutes. Cool completely before serving.