Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9x13-inch baking pan.

Mix flour, baking powder, and salt together in a bowl.

Combine sugar, peanut butter, shortening, and vanilla extract in a large bowl; beat with an electric mixer until smooth and creamy. Add eggs, one at a time, beating briefly after each addition. Gradually add flour mixture, mixing until combined. Fold in nuts and chocolate chips. Transfer batter to the prepared baking pan.

Bake in the preheated oven until top is dry and edges have started to pull away from the sides of the pan, 30 to 35 minutes. Let cool completely before slicing.