In the bowl of a stand mixer, cream together butter and sugars until combined on medium high speed. Add eggs and beat until combined. Use a spatula to scrape down the sides of the bowl. Add vanilla and peanut butter, beating again until combined.
Add in flour, baking soda, baking powder and salt. Mix on low until just combined.
Cover the bowl with plastic wrap and refrigerate for at least 1 hour. The dough can be refrigerated up to 48 hours before baking.
When ready to bake, preheat oven to 350˚F. Line 2 baking sheets with silicone mats or parchment paper.
Roll approximately 1 1/2 to 2 Tbsp of dough into a ball or scoop with a cookie dough scooper. Place balls of dough on baking sheets, spacing them 3 inches apart. You can do the traditional press down of the tops with a fork if you want, but I prefer to skip that step.
Bake for 12 to 18 minutes. Cool for 5 to 10 minutes on the baking sheets, before removing to cooling racks to finish cooling.