Cream the butter and sugars together in the bowl of a stand mixer using the paddle attachment.
Add the peanut butter, egg, and vanilla. Mix well and scrape the bowl.
Combine the flour, baking soda, and salt. Add to the butter mixture all at once and mix until just incorporated.
CHILL dough for 2 hours in fridge or 45 minutes in the freezer. (This keeps the dough thick and puffy / helps it not spread too fast while baking.)
Scoop dough and shape into balls, about 1 rounded Tablespoon each. Place 2-inches apart on silicone lined baking sheets.
Bake at 350˚F for 8 to 9 minutes. Remove from oven. Immediately place a single Hershey Kiss in the center of each cookie while still warm. Rest for 1 minute, then transfer to a wire rack to cool. Store cookies in an airtight container up to 5 days.