Using an electric mixer, combine brown sugar, 1/2 cup granulated sugar, butter, and peanut butter. Beat on medium-high for 1-2 minutes, until the mixture is light and fluffy. Add egg and vanilla and beat again until mixture is smooth.
Sprinkle flour, baking soda, and salt on top of the mixture. Mix on low speed just until combined, scraping the sides and bottom of the bowl once. Stop mixing as soon as the streaks of flour disappear.
Chill dough in the refrigerate for 20-30 minutes.
When ready to bake, preheat oven to 375 degrees F. Line baking sheets with parchment or silicone baking mats, unwrap chocolate kisses, and place remaining 1/3 cup granulated sugar in a small bowl.
Using spoons or a cookie scoop, portion dough into balls of about 1.5 tablespoons each. Roll each gently between your hands to make smooth balls, then roll each in the granulated sugar to coat on all sides. Place on the baking sheets and bake for 8-10 minutes, just until the tops are lightly golden and the tops are crackled.
Remove cookies from the oven, then press a chocolate kiss gently into the center of each cookie. Cool for about 10 minutes on the baking sheets, then transfer to wire racks to cool completely.
Notes
Peanut Butter: Like most cookie recipes, this works best with standard creamy peanut butter - Jif or Skippy, for instance. Avoid using a natural peanut butter if you can - it results in a more crumbly, dry cookie.
Storage: Cookies keep well in an airtight container at room temperature for 3-4 days.