Flour a work surface and knead the cold Sweet Dough 10 to 12 times (see troubleshooting above for why). Shape the dough into a ball, cover the top lightly with flour, and cover with a tea towel and let come to room temperature.
Grease a 9x13-inch pan; if desired, line with parchment paper (this makes for easier cleanup).
In a small bowl, mix the brown sugar, cinnamon, and salt.
Roll the dough into a 16 by 12-inch rectangle. Brush the dough with the melted butter and sprinkle the cinnamon-sugar mixture evenly over the top, pressing it lightly into the butter so it adheres. Starting at a long side, roll the dough into a tight cylinder. Pinch the seam gently to seal it and position the dough seam side down. Use scissors or a sharp knife to cut the dough into 12-equal pieces. Transfer the pieces to the prepared pan and place them cut side up. Cover the pan loosely with plastic wrap and let the dough rise until doubled, 1 to 1 1/2 hours.
Adjust an oven rack to the middle position. Preheat the oven to 350F (180C). Remove the plastic and bake 27 to 32 minutes, rotating the pan halfway through, until the rolls are golden brown. While the rolls are baking, prepare the icing.
Transfer the pan to a wire rack and let cool for 5 minutes. Using an offset spatula or table knife, apply a thin layer of the cream cheese icing, using about one-third of the mixture. Let the rolls cool for another 15 to 20 minutes. Top with the rest of the icing and serve.