Heat milk in the microwave to 105 degrees, about 45 seconds. Use a thermometer to make sure it is not too hot or it will kill the yeast. Add brown sugar and yeast. Pour into the mixing bowl and set aside for 5 minutes or so, until the yeast is nice and frothy.
Add sugar, softened butter, whole egg, and egg yolks and mix until soupy. Add 2 cups of flour and salt and mix with the paddle attachment on low until combined.
Scrape down the bowl and paddle and switch to the dough hook attachment. Add the remaining 2 cups of flour and mix on low for 6 minutes, until the dough is nice and smooth.
Form the dough into a ball and place it in an oiled bowl. Cover and allow to rise for about 2 hours, until doubled in size.
Once doubled in size, punch down the dough and turn out on a lightly floured surface. Using a rolling pin, roll into an 18x12 inch rectangle.
In a small bowl, mix together brown sugar and cinnamon for the filling. Using your fingers or spatula, spread the softened butter evenly for the filling across the dough. Sprinkle the sugar mixture across the dough evenly.
Starting from the bottom, roll the dough up making sure to keep it snug and tight. Using a sharp knife or unflavored dental floss, cut into 12 even rolls. Place evenly spaced in an oiled 9x13 pan and cover with plastic wrap. Refrigerate for 8-12 hours.
Remove rolls from the fridge about 45 minutes to an hour before baking.
Preheat oven to 350 degrees. Remove butter and cream cheese from the fridge and allow to soften on the countertop.
When the oven has reached temp and the rolls are barely touching, bake for 30-35 minutes. If the tops are browning too quickly, a sheet of foil over them can prevent further browning while the rest of the rolls finish baking.
While the rolls are baking, prepare your cream cheese icing. In the bowl of your mixer add cream cheese and butter. Whip together using the paddle attachment until smooth and creamy, about 2 minutes. Add 2 cups of powdered sugar and mix on low until combined. Add additional 2 cups of powdered sugar, vanilla, and salt. Mix at medium/high speed until light and fluffy.
Spread the icing liberally across the almost completely cooled cinnamon rolls.