In a large bowl, cream butter & sugar until light & fluffy. Add egg yolks and vanilla. Stir in flour, salt & nutmeg until combined. Cover & chill dough for approximately 1 hour or until firm & easy to handle.
Preheat oven to 350F; lightly grease a cookie sheet.
Whisk egg whites until foamy. Shape dough intol 1" balls; dip in egg white then roll in walnuts. Place 1" apart on greased cookie sheet.
With the handle of a wooden spoon, make a 1/2" indent in the center of each cookie. Bake 10-12 minutes or until center of cookies are set. Remove cookies from sheet & cool thoroughly on wire racks.
For the filling, combine butter, confectioner's sugar, rum extract & enough milk to make a smooth frosting. Add food coloring if desired. Place frosting into a piping bag fitted with a star tip & pipe into indents of each cookie.