Preheat oven to 350 F.
Line baking sheets with parchment paper or a silpat liner. Set aside.
In medium-sized mixing bowl, beat together butter, sugar, egg, vanilla, and peppermint extract until incorporated.
In a separate bowl stir together flour, baking soda, and salt until combined.
Add flour mixture, milk, and candy canes to wet ingredients and mix until combined.
Shape dough into 1-inch balls. Roll balls in granulated sugar and place on cookie sheet.
Place cookies onto prepared cookie sheets 2 inches apart.
Bake cookies 8-10 minutes until edges are lightly browned. Remove from oven and let rest on pan 2-3 minutes. Place a candy Kiss into the center of each cookie.
Remove cookies from cookie sheets and place on wire rack to cool completely.