Step 1In a large bowl, or in the bowl of a stand mixer, combine the water, yeast and one-half cup flour, stirring to dissolve. Set aside just until the yeast is activated (the mixture will begin to bubble), 5 to 10 minutes.
Step 2While the yeast is activating, combine the remaining flour and 2 1/2 tablespoons sugar in a separate bowl.
Step 3With a fork (if working by hand), or using a mixer fitted with a dough hook, work half of the flour/sugar mixture into the activated yeast, then add the shortening and egg until combined. Slowly add in the remaining flour/sugar mixture (the mixture will at first be stringy, then very sticky as the flour is absorbed). Stir in the salt.
Step 4Move the dough to a floured surface. With floured hands, gently knead the dough (it will be sticky at first) about 5 minutes, adding only as much flour as is needed just to keep the dough from sticking to your fingers or the kneading surface. The finished dough will be tender, soft and slightly tacky.
Step 5Heat the oven to 400 degrees. On a well-floured surface, roll the dough into a rectangle measuring 24 inches by 10 inches.
Step 6In a small bowl, combine the remaining one-third cup sugar with the orange zest.
Step 7Brush the dough with the softened butter, then sprinkle over the orange sugar mixture.
Step 8Roll the rectangle lengthwise into a tight tube (as when rolling cinnamon rolls). Cut the tube into 24 (1-inch) slices, using thread if possible (the thread will slice more easily and cleanly than a knife). Roll the tube one-quarter turn after each slice to keep the tube round; otherwise, it will flatten from all the slicing.
Step 9Place each of the slices into a well-greased muffin tin (the tins must be well-greased or the finished rolls will stick to the bottom). Cover loosely and set aside until the rolls double in size.
Step 10Bake the muffin trays 1 at a time, until the rolls are puffed and golden brown, about 8 to 10 minutes. Rotate the trays halfway through for even baking.
Step 11Cool the rolls slightly, then unmold. Serve warm.