Cream together first four ingredients. Add egg and vanilla. Mix well.
Add flour, baking soda, and salt. Mix well.
Shape dough into small balls. Roll dough in granulated sugar. Bake on well greased cookie sheets 8 minutes in 375° oven.
When sides start to crack, it's time to remove from oven. Put chocolate star candy on each cookie. Press candy down firmly. Return to oven for 2 minutes.