Dough: Place milk and 4 tablespoons butter in a microwave safe bowl. Heat on high for about 1 minute 30 seconds. Butter should be mostly melted, but do not boil. Stir and set aside.
In a large mixing bowl whisk together 2 C flour, yeast, white sugar, and salt. When milk mixture has cooled to warm (not hot) add it to the flour mixture along with the egg while the beater (paddle attachment for those using a stand mixer) is running. Beat until well combined, about 1 minute.
Switch to a dough hook if you have one and ad remaining flour only until dough barely leaves the sides of the bowl. It should be very soft and slightly sticky. Continue to let the dough knead for 5 minutes. If you are not using a stand mixer, turn dough out onto floured surface and knead for 5 minutes by hand. Turn dough out onto a floured surface and let rest for about 10 minutes while you make the filling.Filling: It helps to have butter super soft. Mix with brown sugar and cinnamon.
Assembly: Roll dough into a rectangle about 12 x 14 inches. Spread brown sugar mixture (it will be slightly thick, you might have to "crumble" it) over the surface and use your fingers or the back of a spoon to gently spread around. Roll up from the longer side of the rectangle and pinch edges closed. Score the roll into 12 equal pieces and then cut into rolls. Place in a 9 x 13 pan that has been sprayed with cooking spray. Cover pan with a clean towel and let rise in a warm place for about 30 minutes. In the mean time, preheat oven to 350 degrees.
When rolls have finished rising bake for 15-20 minutes or until light golden brown. If desired spread with icing while still warm. Makes 12 rolls.