Melt chocolate over low heat. Remove and cool. Beat butter in small bowl to soften. Gradually beat in 2/3 cup confectioner's sugar, then 1 teaspoon vanilla and the melted chocolate. Beat in 1 1/4 cups flour and 2 tablespoons milk.
Shape a well-rounded teaspoon of dough around each chocolate kiss to cover completely. Place cookies flat side down on greased cookie sheet. Bake for 10-12 minutes or until lightly browned on bottom. Frost cooled cookies.
To Make Frosting: Beat 2 tablespoons shortening till soft, gradually adding 1/2 cup confectioner's sugar. Mix well. Add 1 tablespoon milk and 1/2 teaspoon vanilla extract. Stir in additional confectioners' sugar (around 3/4 cup). Frosting should be fluffy.