With electric mixer, cream butter and sugar. Add egg, milk and vanilla; mix well.
In medium bowl, whisk together flour, baking powder and salt. Add to wet mixture, beating just until combined. Don't overmix. Chill 20-30 minutes.
Preheat oven to 350 degrees F. Use a 2-teaspoon cookie scoop to scoop up some dough and drop it into your hand. Press a chocolate star into the middle and wrap the cookie dough around it. Roll it into a smooth ball, top with half of the candied cherry, and place on a parchment paper-lined baking sheet about 2 inches apart.
Bake for 10-12 minutes or until bottoms are lightly browned. Remove to wire racks to cool.