Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Beat butter, brown sugar, peanut butter, and white sugar together in a bowl until smooth and creamy. Add egg and egg yolk and mix gently. Gradually stir in flour, baking soda, and salt just until batter is mixed. Gently fold chocolate chips and marshmallows into batter. Spread batter into the prepared baking dish.
Bake in the preheated oven until edges are lightly browned, 15 to 20 minutes. The center will set as it cools. Cool completely before slicing, about 30 minutes.