Cut pecan or walnut halves lengthwise; stuff into dates and set aside. In a bowl, cream butter and brown sugar. Beat in egg yolk. Combine flour, baking powder and baking soda; add to creamed mixture alternately with sour cream. Stir in stuffed dates.
Drop by tablespoonfuls with one date per cookie, onto greased baking sheets. Bake at 375° for 7-9 minutes or until golden brown. Cool on wire racks.
In a saucepan, cook butter over medium heat until golden brown, about 5 minutes. Gradually stir in sugar, vanilla and milk. Frost cookies.