Start with the dough: Add the sugar, water and yeast to a bowl of a stand mixer (or large mixing bowl). Whisk together and allow it to dissolve and begin to foam, about 5 minutes.
Once the yeast begins to foam, with the mixer on low speed using the paddle attachment, add the orange juice, oil, egg, and salt. Add the flour until combined, then knead with the stand mixer or your hands for 8-10 minutes.
Scrape down the bottom and sides of the bowl with a silicone spatula and cover the bowl with plastic wrap. Set aside in a warm place for 1 hour. It should be larger, almost double, and have air bubbles. (If using instant yeast, it only needs 30-45 minutes). Punch the air out of the dough and place on a lightly floured surface. Roll into a large 12x18-inch rectangle, about ⅛-inch thick.
Preheat the oven to 350ºF. Lightly grease a 9x13-inch baking pan. Set side. Mix together the brown sugar and orange zest in a small bowl.
Fill the rolls: Spread the butter all over the dough and then sprinkle the brown sugar mixture, gently pressing into the dough so it sticks. Starting on one of the longer sides, roll the dough into a tight log. Then cut into 12 equal rolls and place in the baking dish.
Starting at one of the longer sides of the rectangle, roll the dough into a tight log, then cut into 12 equal rolls and place them in a baking dish. Cover lightly with a towel or plastic wrap and set aside in a warm place for 1 hour. (If using instant yeast, it only needs 30-45 minutes). Bake for 25-30 minutes until golden brown. If needed, cover the rolls with aluminum foil after 15 minutes to avoid over-browning on top. Allow to cool for 5 minutes before adding cream cheese icing.
While the orange rolls bake, making the icing: In the bowl of a stand mixer or large mixing bowl, on medium-high speed, beat together the butter, cream cheese and orange juice using the paddle attachment until smooth.
Reduce the speed to low and add the powdered sugar. Once combined beat on medium speed until smooth and fluffy. Spread over warm rolls. Cover leftover rolls tightly and store for up to 5 days in the refrigerator.