Place the water in the bowl of an electric mixer; sprinkle with yeast. Let stand until foamy, about five minutes. Add shortening, 1/2 cup sugar, and salt to bowl. Attach bowl to mixer fitted with the paddle attachment; beat until combined. Beat in eggs and half of zest until combined.
With mixer on low speed, add flour, 1/2 cup at a time, beating until incorporated after each addition. Transfer to a floured work surface, and knead slightly to form a ball. Transfer to an oiled bowl, cover loosely with plastic wrap, and let rise until doubled in bulk, about one hour.
Punch down dough with your hands, and replace plastic wrap. Refrigerate overnight. About four hours before serving, remove dough from refrigerator, and let stand at room temperature.
Coat three 12-cup muffin tins with cooking spray. In a medium bowl, whisk together remaining 1/2 cup sugar and orange zest with the orange juice and melted butter; set aside. Divide dough into three equal pieces; cover with plastic wrap or a damp kitchen towel.
On a lightly floured work surface, roll out one piece of dough into an 8-by-14-inch rectangle. Let rest a few minutes if dough resists. Brush dough with some of the orange mixture. Starting with one long side, roll dough into a tight cylinder. Cut crosswise into 12 slices.
Repeat process with two remaining dough pieces. Place slices in prepared muffin tins. Cover loosely with plastic wrap sprayed with cooking spray. Let rise until dough fills cups, about 45 minutes.
Preheat oven to 375 degrees. Brush tops of rolls with remaining orange mixture. Bake until golden brown, 10 to 12 minutes. Remove from oven, and serve warm.