- To make the dough: Warm the milk in the microwave for about 1 minute (it should be about 100°F). Pour the milk into the bowl of a stand mixer fitted with the paddle attachment, then stir in the yeast and 1 tablespoon granulated sugar. Let sit until yeast "blooms" and the mixture becomes creamy, about 5 minutes.
- Add the butter, eggs, salt, cinnamon, and remaining ½ cup granulated sugar to the yeast mixture and mix on low speed until combined. Gradually add 4½ cups flour; once it starts to become difficult for the mixer to mix the dough, switch to the dough hook.
- Knead the dough on low speed for 3-4 minutes. The dough should be tacky but not sticky. If it's still sticky, add remaining 1/2 cup flour 1 tablespoon at a time.
- Gently shape the dough into a ball and place in a lightly greased bowl. Cover with plastic wrap and let rise in a warm place until doubled in size, about 1 hour.
- To make the filling and shape the rolls: Lightly grease two 9-inch square baking pans. In a medium bowl, combine the brown sugar and cinnamon. Set aside.
- Turn the dough out onto a lightly floured work surface. Use a rolling pin to roll out into a rectangle, about 12 x 18 inches.
- Spread the softened butter over the dough, leaving a ¼-inch border all around. (If the butter is too difficult to spread, microwave it for a few seconds.)
- Sprinkle the cinnamon-brown sugar mixture evenly over the dough. Tightly roll the dough lengthwise into a log. Using a serrated knife, cut the log crosswise into 18 rolls. Divide the rolls evenly between the two prepared baking pans. Cover and let rise in a warm place for 30 minutes.
- Preheat the oven to 350°F.
- Bake the rolls until puffed and golden brown, 18-20 minutes. Remove from the oven and place on a wire rack.
- To make the frosting: In the cleaned bowl of the stand mixer, combine the cream cheese, butter, confectioners' sugar, milk, and vanilla and beat with the paddle attachment until smooth.
- Spread the frosting over the warm cinnamon rolls and serve at once.
Note: Cinnamon rolls can be shaped the night before baking. Form the rolls and place them in the pans as above. Then, in place of the second rise, cover tightly in plastic wrap and refrigerate. In the morning, remove the pans from the refrigerator and let rise and come to room temperature (this can take up to 2 hours). Bake as above.