Microwave milk for 45-60 seconds in the microwave (about 110 degrees F). Dissolve yeast in warm milk in a large bowl and let it bubble and react for about 5 minutes. Add sugar, butter, salt, eggs, and flour. Mix well. Knead dough into a large ball, using your hands dusted lightly with flour or with a stand mixer for about 5 minutes. Put in a bowl sprayed with cooking spray and cover tightly with plastic wrap. Let rise in a warm place about 1 hour or until dough has doubled in size.
In a small bowl, thoroughly combine brown sugar and cinnamon. Spray surface with cooking spray or sprinkle flour on it. Roll dough into a 16x21 inch rectangle about 1/4 inch thick. Spread dough with 1/3 cup softened butter and sprinkle evenly with sugar/cinnamon mixture. Roll up dough starting with the longer side and cut into 12 large rolls.Place rolls in a lightly greased 9x13 inch glass baking dish. Cover and let rise until nearly doubled, about 30-60 minutes.
Heat oven to 350 degrees. Bake rolls until golden brown, about 18-20 minutes or until center of the roll is cooked. Add more time if not cooked. While rolls are baking, beat together cream cheese, butter, confectioners' sugar, vanilla extract and salt. Spread half the frosting on them while they are still warm so that the frosting melts into the roll and the other half after they've cooled for a couple of minutes.