Preheat oven to 350F and line a large baking sheet with parchment paper.
In a medium-sized bowl, whisk together the almond flour, cornstarch, baking soda and salt.
In a large mixing bowl, use an electric mixer to cream together the peanut butter, butter, brown sugar and granulated sugar, stopping to scrape down the sides of the bowl as necessary. This will take 2-3 minutes.
Add the egg and vanilla and beat until combined.
On low speed, gradually mix in the dry ingredients until just combined.
Use a 1.5 tablespoon cookie scoop to portion out the cookie dough onto a plate or parchment lined tray. Refrigerate for 1 hour.
Place the remaining 3 tablespoons of sugar in a small bowl.
Roll the chilled dough into balls and then roll in the sugar.
Arrange the cookie dough balls on the prepared baking sheet, about 2-3 inches apart.
Bake for 9-11 minutes, or until the cookies are puffed up and just starting to brown.
Let rest on the pan for just a few minutes before pressing a chocolate kiss into the center of each cookie. Carefully transfer the warm cookies to a plate or tray and place in the freezer for 10-15 minutes. This will stop the kisses from melting on the cookies.
Repeat with remaining cookie dough.
Notes
For greater accuracy, I recommend weighing your ingredients. If you don't have a kitchen scale, be sure to use the spoon and level method when measuring.
Chilling the dough for an hour is a must in order to keep these cookies thick and puffy.
It's also better to underbake these cookies than over bake them, as over baking will cause them to dry out.
I recommend using a light colored baking sheet as darker sheets tend to brown cookies too much on the bottom.
Oven temperatures may vary so start checking on the cookies at around 9 minutes