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 16x21-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.
Assemble
Starting at the longer end, roll up the dough; cut into 12 rolls. Place rolls in a lightly greased 9x13-inch baking pan. Cover and let rise until nearly doubled, about 30 minutes.
Meanwhile, preheat the oven to 400˚F (200˚ 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.