Preheat your oven to 375°F (190°C). Ensure your oven rack is in the center position.
In a medium mixing bowl, whisk together the all-purpose flour, baking soda, and salt until well combined. Set aside.
In a large bowl, cream together the softened butter, creamy peanut butter, 1/2 cup granulated sugar, and brown sugar using an electric mixer on medium-high speed until the mixture is light and fluffy.
Add the egg, vanilla extract, and milk to the creamed mixture. Beat on medium speed until the ingredients are fully incorporated and the texture is smooth.
Gradually add the dry flour mixture to the wet ingredients. Mix on low speed just until the flour disappears and a soft dough forms. Do not overmix.
Shape the dough into 1-inch balls, approximately 1 tablespoon of dough per ball.
Place the additional 1/3 cup of granulated sugar in a shallow bowl. Roll each dough ball in the sugar until completely and evenly coated.
Place the sugar-coated balls 2 inches apart on ungreased cookie sheets to allow for slight spreading.
Bake for 8 to 10 minutes. The cookies are done when the edges are a light golden brown and the surfaces have developed small cracks.
Remove the cookies from the oven and immediately press one unwrapped milk chocolate kiss firmly into the center of each cookie. The cookie should crack slightly around the edges as the chocolate is pressed down.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack. Let them cool completely for at least 1 hour until the chocolate has set and firmed up.