In a large mixing bowl, cream together the softened butter, peanut butter, granulated sugar, and brown sugar until light and fluffy. Beat in the egg and vanilla extract until well combined.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry mixture to the wet ingredients, mixing until a soft dough forms. Chill for 30 minutes if the dough is too soft to handle.
Preheat your oven to 350°F (175°C). Roll dough into 1-inch balls and coat each in granulated sugar. Place on a parchment-lined baking sheet about 2 inches apart. Bake for 8–10 minutes, or until lightly golden and puffed.
Immediately after removing the cookies from the oven, gently press a chocolate kiss into the center of each cookie. Allow the cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.