Preheat oven to 350°F.

1. In a medium bowl, use an electric mixer to cream together the butter, ½ cup of the powdered sugar, vanilla, and the peppermint extract.
   
   
2.  Reduce the speed to low and gradually add the sifted flour and nuts.
   
   
3. Wrap dough in plastic and chill while preparing the filling.

4.  In a small bowl, combine the crushed peppermints with 1/2 cup of the powdered sugar. Set aside.

5. In a separate small bowl, combine the cream cheese with milk.
   
   
6. Gradually add the remaining 1/2 cup powdered sugar and 3 tablespoons of the crushed peppermint-sugar mixture. Tint the filling with a drop of red food coloring, if desired.

7. Remove the cookie dough from the fridge and shape it into teaspoon-sized balls.
   
   
8. Create a deep well in the center of each and fill with a heaping 1/4 teaspoon of filling.
   
   
9. Press with your fingers to completely seal the dough over the filling. Place the cookies a few inches apart on ungreased baking sheets.
   
   
10. Bake for 12 to 15 minutes until cookies just begin to turn golden brown.
    
    
11. Remove from the oven set aside until just cool enough to handle.

12.  Roll the warm cookies in the remaining peppermint-sugar mixture; cool thoroughly, then roll again in the peppermint-sugar mixture to form an even coating.
    
    
13. Store, tightly covered, at room temperature for up to 1 week.