In a medium bowl, whisk together the flour, baking soda, and salt. Set aside.
In a large mixing bowl, beat together the butter and brown sugar until fluffy, about 1 minute. Add the egg and beat for 30 seconds. Add the peanut butter and vanilla and mix until well combined.
Add the dry ingredients to the wet ingredients in two additions, mixing after each addition until everything is incorporated. Chill the cookie dough for 30 minutes in the fridge.
Preheat your oven to 375 degrees F. Line a baking sheet with parchment paper or a silicone baking mat. Place the sugar into a small bowl.
Use a small cookie scoop or measuring spoon to scoop the dough into 1 tablespoon portions. Roll the dough into balls and then roll each ball in the sugar until coated.
Place the dough balls onto the prepared baking sheet about 1-1/2 inches apart. Bake for 8 minutes.
Remove the cookies from the oven and let them cool for 2 minutes (NO LONGER!!). Then press a Hershey's kiss into the center of each cookie until the edges crinkle.
Transfer the cookies to a wire rack to cool completely. The kisses will look a bit soft from the heat of the cookie. That's okay, they will set up as the cookies cool.