Make the dough. In a large mixing bowl or the bowl of a stand mixer, combine warm milk, eggs, and melted butter. Add 2 cups of flour, salt, white sugar, and yeast. Mix until smooth. Gradually add the remaining 2 1/2 cups flour, mixing until a soft dough forms.
Knead the dough. Turn the dough out onto a lightly floured surface and knead for 5-7 minutes until smooth and elastic. (Or use a stand mixer with a dough hook for 5 minutes on medium speed.)
Let it rise. Place the dough in a greased bowl, turning once to coat. Cover with a clean kitchen towel or plastic wrap and let rise in a warm place until doubled in size, about 1 hour.
Roll out the dough. Punch down the dough and turn it out onto a lightly floured surface. Roll into a 16x21-inch rectangle (about 1/4 inch thick).
Make the filling. In a small bowl, mix together brown sugar and cinnamon. Spread the softened 1/3 cup butter evenly over the dough rectangle, leaving a 1/2-inch border. Sprinkle the cinnamon-sugar mixture evenly over the butter.
Roll and slice. Starting from the long side, tightly roll up the dough into a log. Pinch the seam to seal. Using a sharp knife or unflavored dental floss, cut the log into 15 equal slices (about 1 1/2 inches thick).
Arrange in pan. Grease a 9x13-inch baking pan. Place the cinnamon roll slices cut-side up in the prepared pan, spacing them slightly apart (they'll expand as they rise).
Refrigerate overnight. Cover the pan tightly with plastic wrap or aluminum foil. Refrigerate for 8 hours or overnight. The rolls will rise slowly in the fridge.
Bring to room temperature. In the morning, remove the pan from the refrigerator and let it sit at room temperature for 30 minutes while you preheat the oven.
Bake. Preheat the oven to 400°F (200°C). Bake the cinnamon rolls for 18-20 minutes, until golden brown on top.
Make the frosting. While the rolls bake, beat together cream cheese, 1/4 cup softened butter, powdered sugar, vanilla extract, and salt until smooth and creamy.
Frost and serve. Remove the rolls from the oven and let them cool for 5-10 minutes. Spread the cream cheese frosting generously over the warm rolls. Serve immediately and enjoy!