Heat chocolate pieces and shortening in a heavy, small saucepan over low heat until just melted. Cool slightly. With a narrow metal spatula, spread about 1 teaspoon chocolate mixture over flat side of half of the cookies. Place coated cookies chocolate side up on wire rack to set.
Place a small scoop of sorbet (about 1 rounded teaspoon) over chocolate side of each coated cookie, using a melon baller. Dip the melon baller into water between scoops to make the scoops come out neatly. Top sorbet with another cookie to make a sandwich. Cover and freeze at least 1 hour or up to 4 hours. Makes 12 sandwiches (6 servings).