In the bowl of a stand mixer fitted with the dough hook attachment, stir together the warm milk, granulated sugar, and yeast. Let stand until foamy, about 10 minutes.

Add the flour, orange juice, cooled butter, egg, vanilla extract, and salt. With a spatula, mix by hand until all of the flour is incorporated and a shaggy dough forms.

Place the bowl on the stand mixer and mix on low speed for 5 to 7 minutes, until the dough is smooth, wraps around the dough hook and pulls away from the sides and bottom of the bowl.

Remove the dough from the mixing bowl and spray the bowl with nonstick spray. Return the dough to the bowl and cover it with plastic wrap. Let rise in a warm place (about 75°F) for 1 hour to 1 hour and 15 minutes or until nearly doubled in size.

In a small bowl, stir to combine the sugar and flour. Mix in the orange zest.

Lightly grease a 9×13-inch baking pan with softened butter.

Turn the dough onto a lightly floured surface. Press and stretch the dough into a rectangular shape. With a rolling pin, roll the dough into a 12x18-inch rectangle, about ¼-inch thick.

Spread the softened butter onto the dough in an even layer, leaving a ½-inch border on the long side, farthest away from you. Sprinkle the orange-sugar mixture evenly over the butter.

Starting with the long side closest to you, roll the dough into a tight log. Cut the log into 12 pieces of equal width (about 1½ inches wide).

Place the rolls cut side down evenly spaced in the prepared baking dish.

Cover with plastic wrap and let rise in a warm place (75°F) for 45 minutes to 1 hour, until the sides are touching and the rolls are puffed.

After 30 minutes of rising, preheat the oven to 350°F.

Uncover the rolls and bake for 22 to 25 minutes or until lightly browned on top. Let cool for 20 minutes.

Meanwhile, in a large bowl whisk to combine the powdered sugar, 5 tablespoons of orange juice, butter, vanilla, orange zest, and salt. If the icing is too thick, whisk in the remaining 1 tablespoon of orange juice.

Spread the glaze over the warm rolls. Serve warm.