To make the dough: In a large mixing bowl, combine 3 cups (360g) of the flour, the sugar, salt, and yeast.
Heat the milk, water, and butter until the butter softens; make sure the mixture isn't hotter than 120°F so that it doesn't kill the yeast.
Add the liquid ingredients to the flour mixture, along with the eggs.
Beat for 2 minutes; the mixture will be soupy.
Gradually beat in enough of the remaining flour to make a soft dough. In the winter, or under less humid conditions, you may not need all the flour; in the summer, or when it's humid, you'll probably use it all.
Knead the dough until it's smooth, elastic, yet still quite soft, about 6 to 8 minutes. Cover it, and let it rest for 1 hour until puffy.
To make the filling: Whisk together the sugar and cinnamon. Set it aside.
Lightly grease two 9" x 13" pans; or a 9" x 13" pan and two 9" round cake pans.
Divide the dough in half. Working with one piece at a time, pat/roll the dough into a 10" x 15" rectangle. It's a soft dough, and should handle easily.
Spread with half the softened butter (2 tablespoons). Sprinkle with half the cinnamon sugar.
Starting with a long side, gently roll the dough into a log, pinching the edge to seal as well as you can.
Cut the log into 12 pieces (for larger rolls) or 15 pieces (for smaller rolls), and space them in the prepared pan.
Repeat with the remaining dough and filling.
Cover the pans, and let the rolls rise until they're nearly doubled, about 45 to 60 minutes. Towards the end of the rising time, preheat the oven to 350°F.
Bake the rolls for 20 to 25 minutes, until they're golden brown. Remove them from the oven, and cool them for at least 20 minutes before frosting.
To make the frosting: Combine the frosting ingredients, using enough milk to make a soft, spreadable frosting.
Spread the frosting on the rolls. Serve immediately; or cover loosely, and serve later.
Storage information: Store well-wrapped, at room temperature, for several days; freeze for longer storage.