Prepare the dough by placing milk, eggs, margarine, flour, salt, white sugar, and yeast in the pan of a bread machine in the order recommended by the manufacturer. Select the "Dough" cycle and press "Start".
After the "Dough" cycle is complete, turn it out onto a lightly floured surface. Cover it plastic wrap and let it rest for 10 minutes.
Roll the dough on the lightly floured surface into a 14" x 20" rectangle.
Prepare the filling by combining brown sugar and cinnamon in a small bowl. Spread softened/melted butter over the dough, then sprinkle cinnamon-sugar mixture evenly over top.
Starting at a longer edge, roll up the dough and cut it into 12 rolls. First cut the roll in half, then half again. Finally, cut the quarters into three equally thick rolls. Place the rolls in a lightly greased (with some of the remaining butter) 9"x13" baking pan. Place in a warm oven (approximately 100℉-120℉ and let the rolls rise until they have nearly doubled in size. This takes about 45 minutes.
Once the rolls have risen, remove the baking pan from the oven and preheat it to 400℉.
Bake rolls in the preheated oven until golden brown which takes about 15 minutes.
While the rolls are baking, prepare icing by beating powdered sugar, butter, cream cheese, confectioners' sugar, vanilla, and salt until creamy.
Spread some icing on a warm cinnamon roll before serving.