Preheat oven to 350 degrees F (175 degrees C). Spray a 9x13-inch baking dish with cooking spray.

Beat peanut butter and butter together in a bowl with an electric mixer until smooth. Gradually beat brown sugar into peanut butter mixture. Beat eggs into peanut butter mixture 1 at a time, beating well after each addition; add vanilla extract.

Gradually sift flour into peanut butter mixture and mix until batter is well-combined. Pour batter into prepared baking dish and spread evenly in the dish.

Bake in the preheated oven until a toothpick inserted into the center of the blondies comes out clean, about 35 minutes. Cool in the baking dish for 15 minutes before slicing into 24 bars. Remove to a wire rack to cool until just warm.