In a medium bowl, whisk together all-purpose flour, cornstarch, salt, and baking soda; set aside.
In a bowl fit with a mixer, cream butter, peanut butter, granulated sugar, and brown sugar; about 5 minutes on medium high.
Beat in eggs, one at a time. Beat in milk, and vanilla extract until combined; about 2 minutes.
Slowly beat flour mixture into wet ingredients. Mix just until incorporated.
Cover bowl and refrigerate for 5 hours or overnight.
Preheat oven to 375 degrees F. Line a baking sheet with parchment paper or lightly grease.
Using a cookie scoop ( I used 3/4 tablespoon scoop ) scoop dough. Roll into ball then roll into a bowl with granulated sugar. Place on baking sheet.
Bake in oven for 8 minutes. Remove and place chocolate kiss in center of cookie. Return to oven for 3 minutes.
Allow cookies to cool then transfer to a cooling rack. Store in an airtight container once cool.