To your stand mixer bowl, add in the yeast, milk, sugar, egg, salt, butter, and about 3 cups of the flour and mix on low speed until just combined. Add in the remaining flour about 1/2 cup at a time, mixing well after each addition, until the dough is soft, pulls away from the sides of the bowl and when your finger touches the dough, there is no dough transfer on your fingertip. When making bread, the flour is an approximation so this may be around 4 cups, or closer to 5. When the dough reaches this stage, remove it from the mixer bowl and place it in a lightly greased clean bowl. Cover and let rise for about 1 hour.
On a lightly floured work surface, roll out the dough into a large rectangle, approximately 12x18" in size and 1/4" in thickness. Spread the dough with the softened butter, leaving a 1" margin along the sides. In a medium bowl, mix together the brown sugar and ground cinnamon until combined. Liberally sprinkle the brown sugar mixture evenly over the plane of dough.
Starting on the long end closest to you, roll the dough tightly into a log shape away from you and pinch the ends together to seal. Using a sharp serrated knife or unflavored dental floss (my preferred method), cut the log into 12 equal pieces, discarding any ends that may not have been filled or coated. Place the dough spirals into a greased 13x9" light metal baking pan.
Cover the baking pan with a clean cloth and let rise about 30-45 minutes or until almost doubled in size. Meanwhile, preheat your oven to 350° F.
Bake the rolls uncovered for about 20 minutes or until the tops are just barely golden brown and the centers are bubbling. Remove from the oven and immediately frost with the cream cheese glaze. Let stand for about 5-10 minutes before serving.
For the cream cheese glaze: In a large bowl, beat together the butter, cream cheese and vanilla with a handheld electric mixer until combined, about 30 seconds. Add in the confectioners' sugar and milk and mix on low speed until just blended.