Preheat oven to 350 degrees F. Line 2 baking sheets with parchment paper; set aside.
In the bowl of a stand mixer, cream together the butter, 3/4 cup of granulated sugar and the brown sugar together until creamy and fluffy, about 1 minutes. Add in the peanut butter and mix well, followed by the egg and vanilla, mixing well after each addition. Lastly, add in the baking soda, salt, and flour and mix on low speed until a soft dough comes together.
Using a Tablespoon-size cookie dough scoop, scoop out a ball of dough and roll it in the remaining 1/3 cup granulated sugar, coating all sides. Place 1" apart on the baking sheets.
Bake for 8-10 minutes, rotating pans halfway through baking time to ensure even cooking. Let stand on the baking sheet for about 5 minutes, then very gently press an unwrapped Hershey Kiss candy in the center of each cookie. Allow the cookies to cool completely and the Hershey Kiss to set back up on wire racks before serving.