Preheat oven to 375°F (190°C). Line baking sheets with parchment.
Whisk together flour, potato flakes, baking soda, baking powder, and salt in a bowl.
In a stand mixer or in a bowl using a hand mixer, beat butter, granulated sugar, and brown sugar until fluffy. Add peanut butter, then egg, milk, and vanilla.
Stir in dry ingredients until dough forms. It should be soft but not sticky; if tacky, chill 30 minutes.
Roll dough into 1-inch (2.5 cm) balls. Roll each ball in granulated sugar and place on baking sheet, spacing 2 inches apart.
Bake for 8–9 minutes until edges are set but centers are still soft.
Immediately press a chocolate kiss into the center of each cookie. The cookie will crack charmingly around the edges.
Let cool on tray for 2 minutes, then transfer to rack. Serve and enjoy!