Lightly coat a baking sheet with cooking spray; set aside. Flatten thawed rolls into 4-inch rounds. Using a 3-1/2- to 4-inch cookie cutter, cut rolls into star shapes. If desired, shape small scraps of dough into balls. Moisten star points with water and attach dough balls to the points of the stars.
Place stars 2 inches apart on prepared baking sheet. Cover and let rise in a warm place until nearly double (30 to 40 minutes). Bake in a 350 degree F oven for 10 to 12 minutes or until golden. Transfer rolls to a wire rack. Cool completely.
Split rolls in half. Layer ham and cheese on bottom halves of rolls. Using a sharp knife, trim meat and cheese even with edges of rolls. Spread with dressing and add top halves of rolls. Wrap each sandwich tightly in plastic wrap. Pack in insulated containers with ice packs. Makes 4 sandwiches.