Heat milk and butter in microwave or on stove until butter is melted. Let mixture cool to about 110-115 degrees F.
Add warm milk mixture to bowl of stand mixer with the dough-hook attached and sprinkle the yeast on top.
In a separate bowl, whisk together 3 ½ cups of the flour with the sugar and salt until combined.
Add flour mixture to the milk mixture long with the eggs and mix on low until just combined. Then let ingredients rest for a few minutes to allow the dry ingredients to combine with the wet ingredients.
Beat the dough on medium speed adding more flour a tablespoon at a time as needed until it begins to form a ball and pulls away from the sides. Continue for around 5 minutes.
Spray a large bowl with cooking spray and scrape the dough into the bowl and cover with a damp towel.
Let dough rise in a warm spot for until about doubled in size, around 30-45 minutes.
While the dough is rising, make the filing. In a small bowl, add butter, brown sugar and cinnamon and stir until combined then set aside
After the dough has risen, flour your work surface or pastry mat and turn out the dough. Sprinkle the top of the dough with a little flour and roll into a large rectangle. Aim for around 24 x 15.
Using a rubber spatula, spread the filling mixture evenly over the dough.
Starting on the long end roll the dough up tightly. Cut into 12 equal rolls and arrange in a greased 9 x 13 baking pan.
Cover the rolls and allow them to rise for around 20-30 minutes.
While the rolls rise, preheat the oven to 375 degrees.
Add the risen rolls to the oven and bake on the center rack for 15-20 minutes until golden brown. Remove from oven and allow to cool.
While rolls cool prepare the icing by combining cream cheese, butter, and vanilla in a large bowl and mix with a hand mixer until combined.
Add the powdered sugar 1 cup at a time and mix until combined. Add milk to thin if desired
After the rolls are cooled, spread the frosting over top to cover.