Preheat oven to 375 degrees. Line two baking sheets with parchment paper or silicone mats. Place 1/2 cup sugar in a shallow dish.
In a standing mixer with the paddle attachment at medium speed, or with an electric hand mixer, combine flour, brown sugar, remaining 1/2 cup white sugar, baking soda, and salt.
Reduce speed to low and add peanut butter, shortening, egg, milk, and vanilla until stiff dough forms. Shape dough into 1-inch balls, roll in sugar, and place on prepared baking sheets 2 inches apart.
Bake until golden brown, about 10 to 12 minutes, rotating baking sheets after 5 minutes. Remove from oven and immediately press 1 Hershey's® Kiss into the top of each cookie so the cookies crack around the edges. Cool completely on wire racks.