In a large bowl combine water, yeast & 1/2 cup flour, stirring to dissolve, then set aside for 5 to 10 minutes or just until yeast is activated (i.e. when mixture begins to bubble).
While yeast is activating, in a separate bowl, combine the remaining flour & 2 1/2 tablespoons of sugar.
With a fork work half of this flour/sugar mixture into the activated yeast, then add the shortening & egg until combined, before slowly adding the remaining flour/sugar mixture ~ At first it will be stringy, then very sticky as the flour is absorbed. Then stir in the salt.
Move the dough to a floured surface, & with floured hands, gently knead the dough for about 5 minutes, adding ONLY as much flour to the sticky dough as needed to keep the dough from sticking to your fingers or the kneading surface. The finished dough should be tender, soft & slightly tacky.
Preheat the oven to 400 degrees F, then well-grease 2 muffin tins (12 muffins each).
On a well-floured surface, roll the dough into a rectangle measuring 24 inches by 10 inches.
In a small bowl, combine the remaining 1/3 cup of sugar & the orange zest.
Brush the dough with the softened butter, then sprinkle the orange sugar mixture over the buttered surface.
With your hands, roll the rectangle lengthwise into a tight tube, then cut the tube into 24 (1-inch) slices, using thread if possible, as it will slice more easily & cleanly than a knife. Roll the tube one-quarter turn after each slice so that the tube doesn't begin to flatten out.
Place each of the slices into the prepared muffin tins, then cover loosely & set aside until rolls have doubled in size.
Bake muffin trays 1 at a time for about 8 to 10 minutes, until rolls are puffed & golden, being sure to rotate the trays halfway through for even baking.
Cool the rolls in the tins on a wire rack slightly, then unmold & serve warm.