Heat oven to 350°F.
Separate dough into 5 rolls. Cut each roll into 4 thin slices, and place on ungreased cookie sheet.
Bake 10 to 12 minutes or until golden brown. Cool completely.
In medium bowl, mix icing, 1 1/2 cups of the powdered sugar, the vanilla and half of the milk. Beat to form a thick creamy filling, adding remaining powdered sugar or milk as needed.
Spread filling sandwiched between 2 of the cookies, bottom sides together; repeat to use up ingredients. Best served the same day.