Add the butter, peanut butter, and granulated sugar to the bowl of a stand mixer fitted with a paddle attachment. Beat on medium high speed until combined. Note: if you don't own a stand mixer, you can use a large mixing bowl with a handheld electric mixer.
Add in the eggs and vanilla extract and beat until all of the wet ingredients are combined. Scrape the sides of the bowl with a rubber spatula.
In a separate bowl, stir together the almond flour, baking powder, baking soda, and sea salt. Transfer the dry ingredients to the mixer and beat on medium speed until combined.
Refrigerate the dough for 20-30 minutes to allow it to set up. This prevents the cookies from spreading too much during the baking process.
Preheat the oven to 350 degrees Fahrenheit and line two large rimmed baking sheets with parchment paper.
Use a small cookie scoop to scoop the peanut butter cookie dough onto the prepared baking sheet. Be sure to position the mounds of cookie dough at least 2 inches apart on each cookie sheet to allow them room to spread.
Bake for 9-11 minutes in the preheated oven, or until the edges are just barely golden brown. I bake mine for 10 minutes, which results in the perfect chewy and soft texture. Remove cookies from the oven and place them on a wire rack to cool.
