In a medium mixing bowl beat butter and plain cream cheese with an electric mixer on medium to high speed for 30 seconds. Add sugar and vanilla. Beat until combined, scraping sides of bowl occasionally. Using a wooden spoon, stir in the flour.
Divide dough in half. Shape each half of dough into a 6-inch-long roll. Wrap rolls in plastic wrap or waxed paper. Chill in the refrigerator for 4 to 48 hours.
Using a sharp knife, cut dough into 1/4-inch-thick slices. Place slices 2 inches apart on an ungreased cookie sheet.
Bake in a 375 degree F oven for 8 to 10 minutes or until edges are lightly browned. Cool on cookie sheets for 1 minute. Transfer to wire racks to cool completely. Just before serving, spread cookies with strawberry cream cheese and, if desired, top with strawberry halves. Makes about 48.