Stir together the hot water, yeast, and sugar until the yeast is mostly dissolved. Let the mixture stand for about 5 minutes, or until a thick layer of foam develops on the surface.
Once the yeast is activated (as indicated by the foam on top), whisk in the milk and melted butter.
In a separate large bowl, stir together 1 cup of flour and the salt. Pour the liquid ingredients into the bowl with the flour and stir until smooth.
Begin adding more flour, ½ cup at a time, until a sticky ball of dough forms and it becomes difficult to stir with a spoon. Turn the dough out onto a lightly floured surface.
Knead the dough for 3 minutes, adding a small amount of flour as you go to prevent the dough from sticking. After kneading for a couple of minutes, the dough should be very soft, fairly smooth, and just slightly tacky. Do not over-knead the dough or add too much flour, as this will make the dough stiff. You'll use about 2 cups of flour total from the beginning in the bowl to the end of kneading.
Place the kneaded dough back into the mixing bowl and cover loosely with plastic. Let the dough rise for one hour, or until it's double in size.
Punch the dough down to deflate, then scrape it out onto a floured surface. Roll the dough out into an 8x13-inch rectangle, sprinkling with flour as you go to prevent sticking.
To make the filling, stir together the room-temperature butter, brown sugar, cinnamon, and salt until it forms a smooth paste. Spread the paste over the dough from edge to edge.
Roll the dough up (long side toward long side) to create a 13-inch long log. Do not roll tightly, or this will make the center of your cinnamon rolls pop up while baking. Slice the roll into 9 pieces, about 1.5 inches wide each.
Place the slices into a greased 9x9-inch baking dish (or a round pie dish). Let rise for 10-15 minutes as you preheat the oven to 350ºF. The rolls will rise quite a bit in the oven, so don't worry if they're still quite small after 10 minutes of rising.
Once the oven is preheated, bake the cinnamon rolls for 30 minutes, or until they are golden brown on top.
To make the icing, beat together the room-temperature cream cheese, butter, milk, and vanilla until smooth. Begin stirring in the powdered sugar, ½ cup at a time, until it is all incorporated.
After the cinnamon rolls have baked, let them cool for 5-10 minutes before spreading the cream cheese icing on top. Enjoy warm or wait until cooled, then dig in!