Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper or lightly grease them.
In a large mixing bowl, cream together the softened butter, peanut butter, granulated sugar, and brown sugar until the mixture is light and fluffy.
In a separate bowl, whisk together the flour, baking soda, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until a soft cookie dough forms. Be careful not to overmix; just mix until the flour is fully incorporated.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden. The cookies may appear slightly undercooked in the center, but they will firm up as they cool.
Allow the cookies to cool on the baking sheets for a few minutes before transferring them to wire racks to cool completely. Enjoy!