Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper. Unwrap all your chocolate kisses so they’re ready when needed.
Cream together the butter and peanut butter in a large mixing bowl using an electric mixer on medium speed until smooth and well combined, about 1-2 minutes.
Add both sugars and continue beating until the mixture becomes light and fluffy, approximately 2-3 minutes. This creates air pockets for a tender cookie texture.
Beat in the egg and vanilla extract until fully incorporated and the mixture looks smooth, scraping down the sides of the bowl as needed.
In a separate bowl, whisk together the flour, baking soda, and salt until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Avoid overmixing which can make your cookies tough.
Pour some additional granulated sugar into a small bowl. Shape the dough into 1-inch balls and roll each ball in the sugar until completely coated.
Place the coated dough balls about 2 inches apart on the prepared baking sheets to allow room for spreading.
Bake for 8-10 minutes until the edges are just set and the cookies appear light golden. They should look slightly underdone in the center.
Remove from the oven and immediately press a chocolate kiss into the center of each cookie, pushing down gently but firmly. The cookie will crack slightly around the edges – this is exactly what you want!
Allow the cookies to cool on the baking sheet for 2 minutes, then transfer to a wire rack to cool completely. The chocolate kiss will remain soft for quite a while.