Warm the milk and butter on the stovetop or in the microwave until it is warm but not hot to the touch (it should be below 110°F). Add 1 tablespoon of sugar and the yeast to the milk, stirring to combine, then set it aside for 5 minutes.
In a stand mixer fitted with the dough hook attachment, mix together the flour, cinnamon, salt and remaining 1/2 cup sugar. Add the yeast mixture and eggs and mix for 8 minutes until dough is smooth. (The dough will be slightly tacky.) Place the dough in a clean, greased bowl and cover it with plastic wrap. Place the bowl in a warm, dark place to proof until it has doubled in size, about 1 hour.
Grease a 9x13-inch baking dish with butter.
Lightly flour your work surface then scrape the dough out, and using a rolling pin, roll the dough into roughly a 12x20-inch rectangle that is 1/4-inch thick.
Brush the melted butter generously over the dough.
In a small bowl, whisk together the brown sugar, sugar and cinnamon then sprinkle it atop the melted butter. Starting at the long edge of the rectangle, roll the dough up into a tight log, then using a sharp knife, slice the log into 12 2-inch rounds.
Arrange the rounds in the prepared baking dish (discarding any smaller ends). Cover the baking dish with plastic wrap and place it in a warm, dark place to allow the cinnamon rolls to rise a second time for 30 minutes. (Note: This is the point at which you can cover the pan securely with plastic wrap and refrigerate the rolls overnight. Continue with the recipe as directed on the day of baking.)
Preheat the oven to 350°F.
Bake the cinnamon rolls until they are pale golden, 22 to 25 minutes. (Note: If you are baking the cinnamon rolls directly from the fridge, add about 10 minutes to your bake time.)
While the cinnamon rolls bake, make the cream cheese frosting.