With mixer, cream butter and cheese until well blended. Add flour and beat until smooth. Cover and refrigerate 4 hours or overnight.
Preheat oven to 350 degrees. Grease baking sheets.
Divide dough into 3 equal parts, forming dough into balls. On floured surface, roll out into 12-inch circles. Cut into 12 wedge-shaped pieces. Roll each wedge up starting at the large end.
Place on prepared baking sheet with tips under roll. Bake in preheated oven 30 minutes or until golden.
While butterhorns are baking, in a bowl, combine melted butter, milk, vanilla and powdered sugar until smooth. Spread over tops of slightly warm rolls. Cool completely on wire racks and store in covered containers. Makes 3 dozen. Enjoy!