To prepare cinnamon roll dough, place the yeast and the warm milk in a large bowl, and stir. Let sit for about 5-10 minutes for the yeast to activate. The yeast is activated when a foam cap forms on top of milk. If that doesn't happen, repeat, paying attention to milk temperature and making sure the yeast is fresh.
Using a stand mixer, mix the sugar, butter, salt, eggs, and the flour.
Add the milk and activated yeast to the mixer bowl. Mix well, using a dough hook, until the dough is mixed well and gathered into a ball.
Transfer the dough into an oiled bowl, cover and let rise in a warm place for about 1 hour or until the dough has doubled in size. An oven with the light on provides a sufficiently warm environment.
Preheat oven to 350 F degrees. Lline a 9" x 13" baking pan with parchment paper and set aside.
Transfer the dough to a lightly floured surface and roll out to about 1/4" thick, 18" x 12" rectangle.
Spread the butter evenly across the entire surface, then sprinkle brown sugar and cinnamon.
Starting at a longer side of the rectangle, carefully roll the dough into a 18" long roll. Using a serrated knife, slice the roll into about 1 1/2" pieces.
Transfer the rolls into the baking dish, spacing evenly. Cover and let proof for 30 minutes, until doubled in size.
Bake for about 20 minutes, or until light golden brown. Baking time will greatly depend on the oven and the dough, so it's best to go by doneness and not by time.
Meanwhile, prepare the icing by mixing all its ingredients until light and fluffy.
When done, remove the cinnamon rolls from the oven and cover with icing while they are hot. Serve warm.