Special equipment: an electric mixer with a paddle and dough hook attachment
For the dough: In a small bowl, combine the yeast, hot water and 1 teaspoon of the sugar, whisking to mix. Set aside for 10 minutes, allowing the yeast to dissolve and fully activate. It should bubble around the edges and almost double in size. Meanwhile, in a medium bowl, whisk together the milk, oil, orange zest and juice and remaining 1/4 cup sugar and set aside.
Using an electric mixer fitted with the paddle attachment, combine the flour and salt. Add the yeast mixture and orange juice mixture and beat until the dough forms a ball, 2 to 3 minutes. Switch out the paddle for the dough hook and knead the dough until fairly smooth, 4 to 5 minutes. If the dough is too sticky, add more flour 1 tablespoon at a time.
Lightly coat a large bowl with vegetable oil and add the dough. Cover the bowl with plastic wrap and allow the dough to rise until it doubles in size, about 1 hour at room temperature.
Spray a 9-by-13-inch baking dish with cooking spray.
For the filling: On a lightly floured surface, roll the dough into a large rectangle about 1/4 inch thick and slightly bigger than the baking dish. Spread the butter over the dough, leaving a 1/4-inch border on all sides. Sprinkle the dough with the brown sugar, then the cinnamon. Starting with one longer edge, roll the dough into a cylinder and pinch the ends together to seal completely. Cut into 12 rolls and place in the prepared baking dish. Cover the dish with plastic wrap and allow the rolls to rise until they double in size, about 30 minutes at room temperature.
Preheat the oven to 350 degrees F.
Remove the plastic wrap from the rolls and bake, uncovered, until light brown, 25 to 30 minutes.
For the glaze: Meanwhile, in a medium bowl, whisk together the confectioners' sugar and orange juice until smooth. While the rolls are still warm, drizzle them with the glaze and serve.
Adapted from "Trisha's Table: My Feel-Good Favorites for a Balanced Life" by Trisha Yearwood © Clarkson Potter 2015. Provided courtesy of Trisha Yearwood. All rights reserved.