Make the Dough: Pour the milk into the bowl of a stand mixer (or large mixing bowl). Sprinkle the yeast over the milk, then add the sugar, melted butter, egg, and egg yolk. Use a wooden spoon to mix everything together. Add the flour and salt and stir with the wooden spoon until a shaggy dough is formed.
Using the dough hook, knead on medium-low speed until a smooth, shiny ball of dough is formed, 3 to 6 minutes. (You can also knead by hand until smooth ball is formed.) Place the dough in a greased bowl and cover with plastic wrap. Place in a warm, draft-free spot until doubled in size, 60 to 90 minutes.
Make the Filling: In a small bowl, stir together the melted butter, brown sugar, and cinnamon until the sugar is completely moistened and everything has been thoroughly combined.
Assemble the Rolls: Remove the dough to a clean work surface and roll into a 12x18-inch rectangle. Spread the filling all over the surface of the dough (an offset spatula is perfect for this!), leaving a ½-inch border around the edges.
Starting with the short side of the dough, roll the dough up tightly into a cylinder, sealing the edges by pinching them together. Slice off about ½ to 1 inch of the ends, so you have clean edges.
Using a very sharp serrated knife, slice the log into 12 equal pieces.
Place the cinnamon rolls into a greased 9x13-inch baking pan, evenly spaced apart. Cover with plastic wrap and a kitchen towel, and let rise in a warm, draft-free spot until nearly doubled in size and puffy, 30 to 45 minutes.
Bake the Cinnamon Rolls: Preheat oven to 350 degrees F.
Remove the towel and plastic wrap and bake the cinnamon rolls until lightly golden brown on top and an instant-read thermometer inserted into the center reads 190 degrees F, about 22 to 27 minutes. Remove from the oven and set aside while you make the icing.
Make the Cream Cheese Icing: In a medium bowl, stir together the cream cheese and butter until smooth and combined. Add the powdered sugar and vanilla, and stir vigorously until smooth and the consistency of icing. (You can also mix this using a hand or stand mixer, but if your butter and cream cheese are softened enough, I find it easy enough to do with a large spoon.)
Using an offset spatula, spread the icing evenly over the warm cinnamon rolls. Let sit for at least 15 minutes, then serve warm or at room temperature.
Notes
Pan: I use a 9x13-inch pan to bake the cinnamon rolls. If you prefer your rolls to not be touching and not "pop up" so much, you can bake them on a rimmed half-sheet baking pan where they can be spaced apart.
Flavors and Mix-Ins: See the post above for notes on incorporating things like chocolate chips, chopped nuts, spices, and zest.
Storage: For maximum freshness store your cinnamon rolls in an airtight container or covered tightly with plastic wrap. Rolls can be kept at room temperature for up to 2 days or in the refrigerator for up to 7 days.
Make-Ahead (Overnight): Complete the recipe through step #6 (slicing the cinnamon rolls). Place in the prepared pan, cover with plastic wrap and refrigerate overnight. When ready to bake, bring the cinnamon rolls to room temperature and allow them to rise until doubled and puffy, about 1 hour, before baking as directed.
Freezing Before Baking: Once you cut the rolls and place them in a 9x13 baking pan cover with plastic wrap, then foil and store in the freezer for up to 3 months. Place in the refrigerator overnight before baking to thaw and then set on the counter and allow to come to room temperature before baking.
Freezing After Baking: Allow the rolls to cool completely then cover with plastic wrap and foil. Freeze up to 2 months. Move the rolls to the refrigerator the night before and allow them to thaw. Then heat, frost, and serve in the morning. You can also wrap the cooled rolls individually in plastic wrap, place them in a freezer-safe bag or airtight container, and freeze for up to 3 months. Thaw at room temperature or in the microwave.