Place the flour, milk, shortening, eggs, 2 tablespoons sugar, and salt into the bucket of a bread machine. Place the yeast in the yeast compartment. Set the machine for the dough cycle. Remove the dough to a lightly floured surface, cover, and let rest for 10 minutes. Pat the dough to about ½-inch thickness. Use a pasty cutter (or sharp knife) to divide the dough into 24 equal pieces.
Spray a 13-by-9-inch glass baking dish with vegetable oil spray. Gently shape the dough pieces into balls. Place each ball into the pan. Brush the rolls with butter. Cover and let rise until doubled in size, about 30 minutes. (Or, you may refrigerate the rolls overnight and continue with the recipe in the morning.)
Preheat the oven to 400 degrees.
Brush the rolls with half-and-half. Combine the orange zest and the rest of the sugar in a small bowl. Sprinkle over the rolls. Bake the rolls for 15 to 18 minutes or until the tops are golden. Stir together the confectioner’s sugar and orange juice. Pour this glaze over the tops of the warm rolls.