For the Cookies, mix flour and nutmeg in medium bowl. Set aside. Beat 3/4 cup butter and granulated sugar in large bowl with electric mixer on medium speed until light and fluffy. Add whole egg, egg yolk and vanilla; mix well. Gradually beat in flour mixture on low speed until well mixed. Stir in 1/2 cup of the nuts. Refrigerate 30 minutes or until dough is easy to handle.
Preheat oven to 375°F. Shape dough into 1-inch balls. Roll in egg white then in remaining nuts. Place about 1 inch apart on baking sheets. (Refrigerate remaining dough while baking each batch of cookies.)
Bake 10 minutes or until edges are lightly browned. Remove from oven. Immediately make an indentation in center of each cookie by gently pressing with back of small spoon. Cool on baking sheets 1 minute. Remove to wire racks; cool completely.
For the Eggnog Filling, beat 6 tablespoons butter in medium bowl until softened. Gradually beat in confectioners' sugar until fluffy. Beat in milk, rum flavor and nutmeg. Pipe or spoon about 1/2 teaspoon filling into center of each cooled cookie. Sprinkle with additional nutmeg, if desired.