Heat oven to 450 degrees. Grease pan or coat with baking spray.
In a large bowl, add flour and shortening. Cut shortening with pastry knife until crumbs are the size of peas. Add sugar and blueberries. Blend in enough milk with fork until dough leaves sides of bowl.
Shape dough into 12 balls. Roll each ball between your hands until smooth, about 30 seconds. Place in pan and press down with first two fingers. Bake until golden brown, about 8-12 minutes.
In a small bowl, add confectioner's sugar, vanilla, and 4 tablespoons warm milk; mix until smooth. Pour over warm biscuits.