Add flour, salt, and baking soda together in a medium bowl. Whisk together until combined. Set aside.
Add butter to the bowl of a stand mixer. Beat on medium until light and fluffy - about 1 minute. Add sugars and continue to beat on medium for 2 more minutes. Add egg and beat until combined. Add peanut butter and vanilla and beat on medium until completely combined.
Add flour mixture to wet ingredients and mix just until dough forms. Using a small cookie scoop, scoop 1 tablespoon-sized balls and place on a parchment-lined baking sheet. Refrigerate dough for 30-60 minutes to firm it up before baking.
Once dough had chilled, preheat oven to 350 degrees. Remove balls from fridge and roll into smooth balls and then roll in granulated sugar. Place dough balls about 2 inches apart on two baking sheets lined with parchment paper.
Bake for 10 minutes, or until cookies begin to slightly crack on top. Remove from oven and let cool for 3 minutes. Place Kiss in the center of each cookie and gently push halfway through. Place in fridge to cool the cookies and keep the chocolate from melting. Once cooled, remove from fridge and enjoy! Store cookies at room temperature for up to 3 days.