Preheat the oven to 375°F. Line a 9x13 baking pan with parchment paper and set aside.
Sift together the flour, baking powder, and salt, set aside.
In the bowl of a stand mixer fitted with the paddle attachment or a large mixing bowl using an electric hand mixer, cream together the butter and peanut butter until smooth.
Add the sugar and brown sugar to the bowl and mix until combined. Add the eggs, one at a time, until fully mixed. Add the vanilla, mixing again.
Add the dry mixture slowly and blend until just mixed. Fold in the chocolate chips and peanut butter chips by hand.
Press the cookie dough into the prepared baking pan. Bake for 25-30 minutes or until it passes the toothpick test. If you like them chewy, cook for 5 minutes less.
Let the bars cool completely on a wire cooling rack, then lift the bars out using the parchment paper as a sling. Cut into bars and serve.
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Notes
Store at room temperature in an airtight container for up to 5 days. Freeze for up to 3 months. Best eaten at room temperature.