In a large bowl, beat butter and sugar until fluffy. Add egg. Stir in vanilla extract and crumbled mincemeat. Add dry ingredients. Mix well. Batter will be stiff.
Roll into 1 1/4-inch balls. Place on ungreased cookie sheet, flatten slightly.
Bake 10-12 minutes or until lightly brown. Cover with a glaze of confectioners' sugar, milk and vanilla extract while still warm.