Preheat oven to 350 F. In a mixing bowl, beat the butter with the cream cheese until well blended. Beat in the sugar and vanilla, then stir in the flour until well mixed. Using a 1/2 tablespoon measure, shape the mixture into small balls and place 2" apart on ungreased cookie sheets. Make a small dent in the top of each cookie; carefully place a strawberry half, cut side down, in each indentation. Bake for 12 to 18 minutes or until very lightly browned. Cool on racks.
