To the bowl of a stand mixer, add 3 1/2 cups of flour, yeast, salt, sugar, eggs, butter, and warm milk. Using the dough hook attachment, mix until the flour is incorporated, about 4 to 5 minutes. If the dough is sticky, add the remaining 1/4 to 1/2 of flour. Cover the bowl with plastic wrap and let the dough sit for 15 minutes or up to an hour at room temperature.
Lightly flour a work surface and turn out the dough. Punch it down and roll it into a rectangle about 10 x 15 inches. Spread the 1/2 cup of room temperature butter evenly over the dough. Sprinkle over cinnamon sugar.
Heat oven to 350 degrees.
Starting on the long edge, roll the dough into a log making sure it's as tight as possible. Pinch the edge to seal. Using a sharp knife, cut into 8 rolls. Place in a buttered 3qt rectangle (about 6x8 inch) baking dish. Bake for 30-35 minutes or until rolls are golden brown. Remove from oven and let cool for 10 minutes. Spread icing over warm rolls and serve.
In a small bowl mix together brown sugar and cinnamon until well blended.
Cream Cheese Icing
In a medium-size mixing bowl using a hand mixer or whisk, mix together softened cream cheese, butter, confectioners sugar, vanilla, salt until smooth. If icing is too thick, add another tablespoon of mix.