In a large bowl using an electric mixer on medium speed, cream the peanut butter and butter until light and fluffy, about one minute. Add the brown sugar and beat on high speed for about 2 minutes, scraping down the sides of the bowl as necessary. Reduce speed to medium and add the egg and vanilla; beat until well blended.
Beat in the gluten free flour, baking soda, and salt on low until just combined. Cover the bowl and place it in the fridge for at least 30 minutes and up to overnight.
When ready to bake, preheat oven to 350° F. Line two baking sheets with parchment paper.
Using a teaspoon or a cookie spoon, scoop up generous helpings of dough, roll between your hands to form balls, and place on the baking sheets about 2 inches apart. With a fork dipped lightly in water, press the tines onto the dough to lightly flatten. Sprinkle the tops of the cookies with salt if you wish.
Place in the oven and bake for about 12-15 minutes, until cookies are lightly browned and just set. Remove from oven, let cool 2 minutes on baking sheets, then remove cookies to a rack until they cool completely.
Cookies will keep in an air-tight container for 5 days.
Notes
Slightly underbake - You can adjust the texture of the cookies by making them crisper by baking a bit longer, or softer by underbaking them. I tend to prefer the latter, but it's up to you!
What kind of peanut butter? I always choose a natural peanut butter; I'm lucky enough that I can grab fresh ground peanut butter from my small local grocery store. But you can use any peanut butter in this recipe. If you do use a "natural" peanut butter, make sure to stir in the oil first before adding it to the butter.
Make them vegan - For an easy vegan batch of cookies, use 1 flax egg for the egg and your favorite non-dairy butter for the butter.
Naturally sweet - Swap coconut sugar for the brown sugar.
Dairy-free: Use coconut oil in place of the butter or your favorite non-dairy butter.