Preheat the oven to 350F degrees.
Lightly spray a 9x13 inch (23x28 cm) pan non-stick cooking spray and then with parchment paper, leaving an overhang around the edges. Lightly greasing the pan first stops the parchment from sliding around.
In a large bowl beat together the butter, brown sugar and white sugar until no lumps remain.
Beat in the peanut butter until smooth. Then mix in the eggs and vanilla extract.
Turn the mixer down to low speed and mix in the flour, baking powder and salt. Turn of the mixer and scrape down the sides of the bowl as needed.
Stir in the chocolate chips and peanut butter chips.
Spoon the batter into the prepared pan and smooth the top.
Place in the preheated oven in the middle rack and bake for 30 minutes, or until an inserted toothpick comes out clean or with a few crumbs. It may take anywhere between 25-35 minutes, depending on your oven.
Remove from the oven and place the pan on a wire rack to cool, keeping the bars in the pan. Cool for at least 45 minutes, or cool the pan is room temperature for clean cuts (what's pictured).
To slice the bars, lift them out of the pan using the parchment paper overhang. Place on a cutting board and slice. Store cooled bars in an airtight container for up to 4 days at room temperature.