Unwrap the chocolate Kisses and place them in the refrigerator to chill while you prepare the dough.
Whisk the flour, cornstarch, baking soda, and salt in a medium bowl; set aside.
In a large bowl, beat the softened butter with the dark brown sugar and granulated sugar on medium speed until light and fluffy, 2 to 3 minutes.
Beat in the egg and vanilla until glossy. Add the peanut butter and mix on low just until smooth (do not overbeat or the cookies may spread).
Add the dry ingredients and mix on low until a soft dough forms. Cover and chill the bowl for 15 to 20 minutes to firm slightly.
Meanwhile, preheat the oven to 360°F (182°C). Line two baking sheets with parchment. Stir the turbinado sugar and cinnamon together in a shallow dish for rolling.
Scoop dough into 1-tablespoon portions (about 24), roll into balls, then coat in the cinnamon sugar. Arrange on the prepared sheets 2 inches apart. Lightly flatten each ball to about 3/4-inch thick with the bottom of a glass dipped in the sugar mixture.
Bake one sheet at a time until edges are set and tops look matte but centers are still pale, 8 to 10 minutes. Cool on the sheet for 1 to 2 minutes.
Gently press a chilled chocolate Kiss into the center of each warm cookie. Slide the baking sheet into the refrigerator (or a cool garage/balcony) for 5 to 10 minutes to set the chocolate, then move cookies to a rack to finish cooling.