In a large bowl, cream butter and sugar until light and fluffy, 5-7 minutes. Beat in vanilla. Gradually add flour and mix well. Drop by heaping tablespoonfuls into greased miniature muffin cups; flatten slightly. Press a walnut half into the center of each.
Bake at 350° for 10-12 minutes or until edges are lightly browned. Cool for 2 minutes before removing from pans to wire racks.