Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking pan and set aside.
Whisk the all-purpose flour, baking soda, and salt together in a small bowl until combined; set aside.
In the bowl of an electric mixer, cream together the light brown sugar, creamy peanut butter, unsalted butter, and granulated sugar on medium speed until light and creamy, about 2–3 minutes.
Add the egg and vanilla extract to the creamed mixture and beat until incorporated.
Reduce the mixer speed to low and add the dry ingredients, mixing only until the flour is just incorporated; do not overmix.
Fold in the semisweet chocolate chips and peanut butter chips with a rubber spatula until evenly distributed.
Transfer the dough to the prepared pan and press into an even layer.
Bake for 16–20 minutes, or until the center is set and the edges are lightly golden.
Cool completely in the pan on a wire rack, then cut into 32 bars.