Prepare dough: Place milk, eggs, margarine, flour, salt, white sugar, and yeast in the pan of a bread machine in the order recommended by the manufacturer. Select dough cycle; press Start.
When dough has doubled in size, turn it out onto a lightly floured surface. Cover it with a kitchen towel or plastic wrap and let it rest for 10 minutes.
Roll dough on a lightly floured surface to a 16×21-inch rectangle.
Prepare filling: Combine brown sugar and cinnamon in a small bowl. Spread softened butter over the dough, then sprinkle cinnamon-sugar mixture evenly over top.
Starting at the longer end, roll up the dough; cut into 12 rolls. Place rolls in a lightly greased 9×13-inch baking pan. Cover and let rise until nearly doubled, about 30 minutes.
Meanwhile, preheat the oven to 400 degrees F (200 degrees C).
Bake rolls in the preheated oven until golden brown, about 15 minutes.
While rolls are baking, prepare icing: Beat confectioners’ sugar, butter, cream cheese, confectioners’ sugar, vanilla, and salt until creamy.
Spread icing on warm rolls before serving.
Per Serving: 502 calories; protein 8.2g; carbohydrates 77.3g; fat 18.5g; cholesterol 64.1mg; sodium 387.7mg