Make the dough: In a large bowl, whisk the flour, sugar, salt, and yeast together. Set aside.
Heat the milk and butter together in the microwave until the butter is melted and the mixture is warm to touch (about 120-130°F). Stir in the 2 tablespoons of orange juice, 1 tablespoon orange zest, and the egg. Combine the butter mixture and the flour mixture and stir until it forms a soft dough. Poke it with your finger—it should bounce back. If not, stir in more flour 1 tablespoon at a time.
On a lightly floured surface, knead the dough for 1 minute. Place in a lightly greased bowl (I used non-stick spray) and let rest for about 10 minutes.
Fill the rolls: After 10 minutes, roll the dough out in a 14x8-inch rectangle. Spread the softened butter on top. Mix together the cinnamon, sugar, and remaining orange zest. Sprinkle it evenly all over the dough. Starting with the long edge (14-inch), roll up the dough tightly. Cut into 10-12 even rolls and arrange in a lightly greased 9-inch round cake pan or pie dish.
Loosely cover the rolls with aluminum foil or plastic wrap and allow to rise in a warm, draft-free environment for 60-90 minutes.
Bake the rolls: After the rolls have doubled in size, preheat the oven to 375°F (190°C). Bake for 25-28 minutes* until lightly browned. *Cover the rolls with aluminum foil after 15 minutes to avoid over-browning on top.
Make the glaze: Whisk the confectioners' sugar and remaining orange juice together until smooth. Drizzle or spread over warm rolls.
Cover leftover frosted or unfrosted rolls tightly and store for up to 3 days at room temperature or up to 5 days in the refrigerator.