Preheat oven to 350 degrees F.
Prepare Peppermint Filling: set aside. Prepare Peppermint Topping; set aside.
In a mixing bowl, beat together butter and sugar until smooth and elastic; add vanilla extract. Stir in flour; knead until well mixed. Cover the dough and refrigerate for 1 hour or until the dough is easy to handle.
When ready to roll the prepared dough into balls, remove from refrigerator. Set aside 1/2 cup of dough. Lightly flour your fingers and shape remaining dough into 1-inch balls. Make a deep well in the center of each ball with the handle of a wooden spoon. Fill with 1/4 teaspoon prepared Peppermint Filling.
Use reserved dough to cover filling by placing a small flat disc of dough over the hole. Reshape or roll if necessary into smooth balls.
Place on ungreased cookie sheets, about 1-inch apart, and bake approximately 12 minutes or until set but not brown.
Remove from oven, immediately remove from baking sheet, and roll warm (not hot) cookies in the prepared Peppermint Topping mixture. Set on wire cooling racks to cool completely. Roll in any remaining Topping mixture again (if desired).
Tip for crushing hard peppermint candy: Place candy in a large plastic food-storage bag, and chill in the freezer. Crush candy inside of the bag by lightly pounding with the smooth side of a meat mallet or a small pot.
For the filling, combine cream cheese and milk in a small bowl. Stir in powdered sugar, crushed peppermint candy, and food coloring (if desired); mix well.
In a small bowl, combine powdered sugar and crushed peppermint candy.
Peppermint Snowball Cookie Recipe: https://whatscookingamerica.net/cookie/peppermintsnowballs.htm