1. Beat the 2/3 cup butter in a mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar and the 1/8 teaspoon nutmeg; beat until combined. Beat in egg yolks and vanilla. Beat in as much flour as you can. Stir in any remaining flour with a wooden spoon. If necessary, cover and chill dough about 1 hour or until easy to handle.
2. Shape into 1-inch balls. Roll balls in egg whites, then in chopped walnuts. Place 1 inch apart on lightly greased cookie sheets. Press
centers with your thumb. Bake in a 375 degrees F oven for 10 to 12 minutes or until edges are lightly browned. Cool on wire racks.
3. For filling, beat the 1/4 cup butter until softened. Add powdered sugar and beat until fluffy. Beat in rum or rum extract and enough milk to make of spreading consistency. Spoon or pipe about 1/2 teaspoon filling into center of each cookie. Sprinkle with nutmeg.