Activate the yeast: Get out a large mixing bowl, or simply use the bowl for your stand mixer, and pour in the warm milk, ⅓ cup of sugar and yeast. Stir this together and let it sit for 10 minutes or until the yeast has shown signs of life.
Make the dough: Once the yeast has shown it’s alive, add the flour and ½ stick of melted butter to the bowl. Then use the dough hook attachment, and mix everything together on low for 2 minutes, or until it starts to form clumps. You can also do this without a stand mixer by simply mixing these ingredients with a wooden spoon. Once the clumps have started to form add in one egg and let it mix into the dough completely. Then add in the second egg and allow it to mix in until you have a uniform dough.
Let the dough rise: Get out a separate large bowl and grease the insides with about a tablespoon of canola/vegetable oil. Then place the dough in the center of the bowl and cover it loosely with some plastic wrap. Let the dough rise for an hour or two, then pound it down with your fists.
Make the cinnamon roll: Flour a flat area, place the dough on it and use your hands to pad it down into a rectangular shape. Then use a rolling pin to flatten out the dough until it is ½ an inch thick and roughly 18×24 in size. Next, pour the stick of melted butter over the dough and use a brush to distribute it evenly. Combine the brown sugar and cinnamon in a bowl and then sprinkle that over the butter covered dough. Use your hands to press this mixture in. Finally, roll the dough tightly until you have one long cinnamon roll.
Cut it into rolls: Trim off any excess at the ends of the roll, and then cut the roll in half. Then cut each half in half so that you have 4 medium long pieces. Finally cut each quarter into three evenly sized pieces. Place these rolls in a greased 9×13 pan and cover it with plastic wrap.
Place this in your fridge overnight.
Next morning take the pan out and let the cinnamon rolls rise at room temperature for an hour or two
Preheat your oven to 375 degrees Fahrenheit.
Bake the cinnamon rolls in the oven for 20 to 30 minutes, or until their tops have become golden brown.
Make the icing: While the cinnamon rolls are baking add the softened cream cheese, and soften butter to your stand mixer bowl. Mix these together until they are fully combined. Then add in the vanilla extract and powdered sugar and mix those in until they are fully combined. Finally, add a tablespoon of milk at a time until the icing is as thick or thin as you prefer.
Once the cinnamon rolls have cooked completely take them out of the oven and spread the icing all over the tops of them.
Serve and enjoy immediately!