First, unwrap the kisses and place in a bowl. Place in the freezer.
In a medium bowl, sift the flour, baking soda, and salt. Set aside.
Using a mixer in a separate bowl, beat the butter, brown sugar, and sugar on high speed for 2 minutes. It will become pale in color and fluffy.
Add the peanut butter, vanilla, and egg. Mix on medium until creamy. Add the dry ingredients. Mix on low speed until just combined.
Preheat the oven to 350℉. Line two cookie sheets with parchment paper. Set aside. Let the cookie dough rest for 10 minutes. This helps with spread.
Use a small cookie scoop to scoop the dough. While the cookie dough is still in the scoop, press your thumb in the center. Place a frozen peanut butter dollop into the center. Cover it up, and remove from the scoop. Roll the cookie dough ball in your hands until smooth.
Add the sugar to a bowl big enough to roll the cookie dough balls in. Roll the cookie dough balls in the sugar. Place 9 cookie dough balls per cookie sheet. *Wait to do the rest of the cookie dough until ready to bake, to keep the peanut butter cold.
Bake for 9-11 minutes. Bake until the edges are lightly golden.
Let the cookies sit on the pan for 3 minutes before topping with a frozen Hershey's kiss in the center and then immediately transfer to a cooling rack. Cool completely.