Preheat the oven to 350°F. Line a 9x9-inch baking pan with parchment paper. Leave some paper hanging on the sides, it can help you to remove the peanut butter brownies from the pan. Slightly grease with a non-stick cooking spray. Set aside.
In a mixing bowl, whisk together all-purpose flour, baking powder, and salt. Set aside.
In a separate mixing bowl, using an electric mixer, beat together the peanut butter, margarine, granulated sugar, and light brown sugar until smooth. Then, beat in the eggs and vanilla extract until smooth and well combined.
Add the dry ingredients to the wet. Stir using a rubber spatula until combined.
Transfer the peanut butter mixture to the prepared baking pan. Spread evenly.
Bake in the preheated oven for 20-25 minutes or until slightly golden and the edges are set. You can also check the readiness using a toothpick inserted in the center, if it comes out clean, the peanut butter brownies are ready.
Remove from the oven and place the baking pan on a cooling rack. When cooled to room temperature, remove from the baking pan and slice into 16 squares. Enjoy!