Make the dough: pour the warm milk into a large bowl and sprinkle the yeast over it. Let it sit 5–10 minutes, until foamy — that's the yeast telling you it's alive. Whisk in the sugar, melted butter, eggs and salt.

Stir in 4 cups of flour until a soft, shaggy dough forms. Turn it onto a floured counter and knead 5–8 minutes, adding flour a spoonful at a time as needed, until the dough is smooth, elastic and only slightly tacky.

Place the dough in a greased bowl, cover with a clean towel, and let it rise in a warm spot 1 hour, or until doubled in size.

Stir the brown sugar, cinnamon and pinch of salt together for the filling. Roll the risen dough out on a floured surface into a rectangle about 16 x 21 inches. Spread the softened butter all over it, right to the edges, then sprinkle the cinnamon sugar evenly over the butter.

Starting from a long side, roll the dough up tightly into a log. Pinch the seam to seal. Using unflavored dental floss or a sharp serrated knife, cut the log into 12 even rolls.

Arrange the rolls in a greased 9x13-inch baking pan. Cover and let rise again, 30 minutes, until puffy and touching each other. Meanwhile, heat the oven to 350°F (175°C).

Bake 20–25 minutes, until the rolls are golden on top and the centers are cooked through. Don't overbake — a soft roll is the whole point.

While the rolls bake, whisk the icing ingredients together until smooth and pourable, adding milk a spoonful at a time. Spread the icing over the rolls while they're still warm, and serve right away.