Make the dough: Wisk the flour, sugar, salt, and yeast in a stand mixer or large bowl.

Combine the milk and butter in a heatproof bowl. Microwave or use the stovetop to heat the butter gently until melted, between 105-110°F. If the mixture is too warm, put in the fridge until cooled to the appropriate temperature.

Pour melted butter mixture into the dry ingredients. Stir in stand mixer with dough hook on low until the flour has absorbed the liquid. Add the egg. Mix dough with dough hook for 5 minutes on medium speed, or knead by hand on a lightly floured surface until a soft dough ball is formed.

Lightly grease a large bowl with butter or cooking spray, and cover tightly. Let the dough rise in a warm spot in your kitchen for 1 hour, or until doubled.

Lightly dust a pastry mat and rolling pin with flour. Roll the dough into a 24x14 inch rectangle of uniform thickness.

Spread the softened butter on top with a rubber spatula. In a small bowl, mix the brown sugar and cinnamon, then sprinkle the mixture on top of the dough evenly.

Roll up the dough tightly, starting on the long side. Cut into 12 even slices and arrange on a 9x13 inch baking pan lined with parchment paper. Cover tightly and allow to rise for 2 hours on the counter, or doubled in size. You may also allow them to rise in the refrigerator for 8-12 hours to bake the next morning. (If you refrigerate the dough rolls, leave the rolls on the counter in a warm spot and allow to come to room temperature prior to baking. This will take about 1 hour.)

Remove cinnamon rolls from the oven and allow to cool on a cooling rack for at least 10 minutes. There will be liquid bubbling around the rolls- this is normal. While cooling, prepare the frosting.

In a stand mixer or large bowl, mix the cream cheese, softened butter, confectioners sugar, and vanilla until smooth. Spread the frosting evenly over the cooled rolls. Store cinnamon rolls in an airtight container for up to 3 days, or in the refrigerator for 5 days.