Beat butter at medium speed with an electric mixer until creamy. Gradually add sugar, beating well. Add eggs and egg yolks, 1 at a time, beating until blended.
Add flour to butter mixture gradually, beating at low speed just until blended. Add 2 teaspoons vanilla extract, beating just until blended.
Drop by rounded teaspoonfuls on lightly greased cookie sheets. Press a candied cherry half in center of each cookie.
Bake at 350° for 20 minutes or until golden brown. Remove cookies to wire racks, and let cool.