In a medium bowl, whisk together the gluten-free flour, baking soda and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or use a large bowl with an electric hand mixer), add the butter and beat on high speed for 1 minute until creamy.
Add the brown sugar and granulated sugar and mix on medium-high speed until creamed, about 2 minutes.
Add the egg, peanut butter and vanilla. Beat on medium-high speed until well-combined, another minute or so. Scrape down the sides and bottom of the bowl.
With the mixer running on low, slowly add the dry ingredients to the wet ingredients and mix on low until combined.
Cover the bowl of dough with plastic wrap and chill for at least 1 hour in the refrigerator (and up to 3 days). (If chilling for longer than a few hours, though, allow to sit at room temperature for at least 30 minutes before scooping and baking for the right texture.)
Preheat the oven to 350F. Place the unwrapped chocolate kiss candies in a bowl and set in the freezer (so they hold their shape when you place them on the cookies!).
Line two large baking sheets with parchment paper or silicone baking mats.
Scoop the dough into 1 tablespoon-sized balls. (Don't make them too big or you won't have the right dough/chocolate ratio.) Roll each ball in sugar before placing on the baking sheet, about 2 inches apart.
Bake for 10-12 minutes or until the tops begin to slightly crack. Remove cookies from the oven and immediately press a chocolate kiss candy into each cookie.
Let cool for 5 minutes, then transfer to a wire cooling rack to cool completely.
Repeat with the remaining dough. Enjoy!