Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, cream together the softened unsalted butter, peanut butter, granulated sugar, and brown sugar until the mixture is light and fluffy.
Add in one large egg and one teaspoon of vanilla extract to the creamed mixture, mixing until everything is well combined.
In a separate bowl, whisk together 1 1/2 cups of all-purpose flour, one teaspoon of baking soda, 1/2 teaspoon of baking powder, and 1/4 teaspoon of salt. Gradually add this dry mixture into your wet ingredients while stirring until a soft dough forms.
Roll the dough into small balls and place them on your prepared baking sheet with enough space between each ball for spreading during baking. Use a fork to gently press down on each cookie, creating a crisscross pattern.
Bake the cookies in your preheated oven for about 10-12 minutes or until their edges turn lightly golden brown. Allow them to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.