Prepare the dough. Add the warm milk, granulated sugar, and yeast to the bowl of a stand mixer. Set aside until the yeast has bloomed, about 5 minutes.
Next, add the butter, egg, vanilla, flour, and salt. Turn the mixer on to the lowest speed. Once the dough has started to form, turn the speed to medium and mix for about 5 minutes. The dough should be smooth and elastic. It should bounce back once poked.
Leave the dough in the stand mixer and cover with plastic wrap or a tea towel. Place in a warm place to rise until doubled in size. About 1.5 hours.
Make the cream cheese icing. Place all of the ingredients in a mixing bowl. Using an electric mixer, blend until combined. Set aside.
Assemble the cinnamon rolls. Once the dough has risen turn it out onto a lightly floured surface.
Roll into a rectangle that is approximately 18” long, 12” wide, ¼” thick.
Spread the cream cheese over the dough and then sprinkle the brown sugar and cinnamon over the cream cheese. Then, roll into a tight log starting at one of the long sides. For larger rolls, roll the tight log starting at one of the short sides.
Slice the log into about 1-1 ½ -inch rolls. This will yield about 12 rolls depending on how tightly you roll your log and whether you start rolling at a long or short side of the dough.
Butter a 9x13-inch baking dish or line it with parchment paper. Add the rolls to the dish, making sure they just barely touch. Depending on how tightly you rolled dough into the log, you can either place rolls 3x4 or 2x4 with extra rolls in another baking dish.
If you're making the rolls in advance, wrap them in plastic and place them in the fridge for up to 12 hours. Bring the rolls to room temperature (about 30 minutes) when you're ready to bake and then skip to step 10.
If you are making the rolls immediately, cover them with plastic wrap and then a tea towel. Place them in a warm spot to rise until the rolls begin to touch - about 30 minutes. While the rolls rise, preheat your oven to 350℉.
Bake the cinnamon rolls for 18-22 minutes (depending on your oven and the size of your rolls) or until the centers are set, be sure not to overbake.
Allow the cinnamon rolls to cool for 10 minutes before frosting.