In a large bowl, cream together unsalted butter (6 tablespoons), creamy peanut butter (1/3 cup), baking powder (1/2 teaspoon), xanthan gum (1/2 teaspoon), and salt (1/4 teaspoon) using an electric mixer until light and fluffy (about 6-8 minutes).
Working with the mixer on, add the eggs (2) one at a time.
Again, keep the mixer on, and sprinkle in erythritol (1 cup), working in 4 batches. Allow each batch to incorporate fully before adding the next. Occasionally scrape down the sides with a spatula to fully incorporate all ingredients.
Use this same technique with the almond flour (2 cups).
Roll the dough between 2 sheets of parchment paper until it's 1/8" thick.
Use a round cookie cutter (I used a 1 1/2" round cutter) to cut circles into the dough.
Preheat oven to 350 F.
Place in the freezer for 20 minutes to allow the butter and peanut butter to solidify.
Remove dough from the freezer, and use a spatula to move each cookie onto a rimmed baking sheet, leaving 1/2" between each cookie.
Bake in preheated oven for 12-14 minutes. Allow them to cool completely on the baking sheet (they'll continue to crisp as they cool).
Meanwhile, gather the scraps and repeat the steps above to form cookies.