Dissolve yeast in lukewarm water. Add shortening, egg, sugar, salt, orange rind and juice. Add flour gradually, beating thoroughly after each addition. The dough should be soft but not sticky. Turn out on a lightly floured board and knead until smooth. Place in a greased bowl, cover and let rise in a warm place until double in bulk, about 1 hour. Punch down and turn out on a floured board.
Roll dough about ½-inch thick and cut with 2½-inch round cutter. Let rest for a few minutes. Shape like Parker House Rolls, inserting a piece of orange section in the crease of each roll. Place ½-inch apart in two 8-inch square pans. Let rise in a warm place until double in bulk. Bake at 425 degrees F (425 °F.) for 15 to 20 minutes. Brush with butter and while still warm cover generously with Orange Icing. Makes 2 dozen rolls.
Orange Icing
Combine 1 tablespoon butter, 1 tablespoon lemon juice, 1 tablespoon orange juice and 1 teaspoon grated orange rind. Heat over hot water until butter melts. Remove from heat, stir in 1½ cups confectioners' sugar and beat well.