Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper. In a large bowl, mix together the brownie mix, flour, eggs, oil, and water until a soft, thick dough forms.
Scoop about 1.5 tablespoons of dough per cookie and roll into balls. Place them on the baking sheet and slightly flatten the tops with your hand or the back of a spoon. Bake for 8–10 minutes until set around the edges. Do not overbake—they will continue to cook on the pan. Let cool on the sheet for 5 minutes, then transfer to a wire rack.
While cookies cool, mix peanut butter and powdered sugar in a medium bowl until a thick dough forms. Roll into 1-inch balls (you’ll need one per cookie) and flatten slightly into disks.
Once cookies are mostly cool but still slightly warm, gently press a peanut butter disk into the center of each one.
Melt chocolate chips (and butter if using) in the microwave in 30-second intervals, stirring until smooth. Spoon about 1 teaspoon of melted chocolate over the peanut butter layer and spread slightly with the back of a spoon.
Transfer cookies to the fridge for about 20 minutes to allow the chocolate to set completely before serving.