Cream the softened butter, granulated sugar, and brown sugar together in a large bowl using a hand or stand mixer until smooth.
Add the eggs one at a time, mixing well after each, then mix in the vanilla and peanut butter until fully combined.
In a separate bowl, whisk together the flour, baking soda, baking powder, and salt, then slowly add the dry ingredients to the wet and mix on low until a thick, sticky dough forms.
Cover the dough and chill it in the fridge for at least 3 hours, or up to 2 days if you get distracted and forget about it like I did once.
Preheat the oven to 350°F (177°C) and line two large baking sheets with parchment paper or silicone baking mats.
Roll balls of dough (about 1.5 tablespoons each), roll them in sugar if you like, and place them 2 inches apart on the baking sheets.
Press a fork into the tops to create the classic criss-cross pattern, then bake for 12 to 13 minutes until the edges are lightly golden.
Let the cookies cool on the baking sheet for 5 minutes, then move them to a wire rack to cool completely.