Arrange your oven rack to the middle position. Line 2 large rimmed baking sheets with parchment paper. Preheat your oven to 350°F.
In a medium bowl, whisk the almond flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, use an electric mixer to beat the softened butter and peanut butter until smooth and creamy. Add the granulated sugar and brown sugar and mix until well combined. Wipe the mixer and sides of the bowl with a rubber spatula. Add the egg and extra egg yolk and mix until well combined. Mix in the vanilla extract.
Add the dry ingredients and mix until the dough comes together. The dough will be thick.
Form the dough into 2 tablespoon-size balls and arrange them on your parchment-lined baking sheet, about 2 inches apart. Use a fork to indent each cookie dough ball with a criss-cross pattern.
Bake the cookies, one baking sheet at a time, for 10-12 minutes. Remove from the oven and allow the cookies to cool on the pan for at least 5 minutes before transferring to a plate or a cooling rack.