I haven't tested the recipe using natural peanut butter - I've only used traditional creamy peanut butter (like Jif or Skippy). The trick to this recipe is instead of pressing the cookies flat before baking, give them a light press after they are done baking. It makes all the difference in the world for soft, dense peanut butter cookies.
1 cup (2 sticks, 16 tablespoons) butter, softened to room temperature
2 cups creamy peanut butter (see note)
1 1/2 cups brown sugar (10 1/2 ounces)
1/2 cup granulated sugar (3 1/2 ounces)
2 large eggs
1 teaspoon vanilla extract
Preheat the oven to 350 degrees F.
In a medium bowl, whisk together the flour, salt, baking powder, and baking soda. Set aside.
In a large bowl with a handheld electric mixer or in the bowl of an electric stand mixer fitted with the paddle attachment, beat together the butter and peanut butter until light and fluffy, 1-2 minutes, scraping down the sides of the bowl as needed.
Add the brown sugar and granulated sugar and mix until combined. Beat in the eggs and vanilla until creamy.
Add the dry ingredients and mix until combined.
Scoop the dough and roll into 1- or 2-inch balls. Place on parchment- or silpat-lined (or lightly greased) large, rimmed baking sheets, placing them a couple inches apart.
Bake for 10-11 minutes until puffed. Don't overbake.
Remove from the oven and immediately press each cookie to flatten slightly with the bottom of a flat drinking glass. Don't flatten the cookies to smithereens, just press the puffed part down until the cookies are an even thickness.
Scoop onto a cooling rack to cool completely. These cookies freeze great (and actually taste amazing straight from the freezer).