Beat butter, white sugar, and brown sugar together with an electric mixer in a large bowl until light and fluffy. Beat egg and vanilla extract into the butter mixture. Add peanut butter and beat until incorporated.
Sift flour and baking soda together in a separate bowl; mix into the butter mixture. Fold chocolate chunks into the mixture.
Spread the batter into a 13x9-inch baking dish.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 20 to 25 minutes. Cool completely before cutting into squares.