Preheat your oven to 200°F then turn it off to create a warm environment for proofing. Grease a 9x13 inch baking dish and set aside.
In a large bowl or stand mixer, combine warm milk, sugar, and instant yeast. Let sit for 5 minutes until foamy.
Add eggs, softened butter, flour, and salt. Mix until the dough comes together and then knead for 5–7 minutes until smooth and slightly sticky.
Cover and let the dough rest in the warm oven for 20 minutes.
Make the filling by mixing brown sugar and cinnamon in a small bowl.
After resting, roll out the dough on a floured surface to a 16x12 inch rectangle.
Spread softened butter over the dough. Sprinkle the cinnamon sugar mixture evenly over the surface.
Tightly roll the dough from the long edge to form a log. Slice into 12 even rolls using a sharp knife or unflavored dental floss.
Place rolls in the prepared baking dish. Cover and let rise in a warm place for 15–20 minutes while preheating the oven to 350°F.
Bake for 18–22 minutes, until golden brown and cooked through.
Meanwhile, make the icing: whisk cream cheese, butter, powdered sugar, vanilla, and milk until smooth.
Spread icing over the warm rolls and serve immediately.