Warm milk to about 110 degrees F (45-60 seconds in the microwave). Dissolve yeast with a pinch of sugar in warm milk in a large bowl and let it bubble and react for about 5 minutes.
Add sugar, butter, salt, eggs, and flour. Mix well. Knead dough into a large ball, using your hands dusted lightly with flour or with a stand mixer for about 5 minutes.
Place the dough in a greased bowl, cover and let it rise in a warm place until doubled, about 1 hour. The proof setting on your oven helps if your house is cold.
Stir the brown sugar and cinnamon together. Roll the dough into a 16 x 21 inch rectangle about 1/4 inch thick on a lightly floured surface.
Spread with the softened butter and sprinkle with the cinnamon sugar. Roll up from the long side and cut into 12 large rolls.
Place the rolls in a greased 9 x 13 inch dish. Cover and let rise 30 to 60 minutes, until nearly doubled. If making the night before I let them rise covered with a dish towel on the counter overnight.
Preheat the oven to 350°F. Bake 20 to 30 minutes, until golden brown and cooked in the center (center will be 190℉ when done).
While the rolls bake, beat the frosting ingredients until smooth. Spread half over the warm rolls so it melts in, then spread the rest after a few minutes.
Notes
Instant yeast: use 1 3/4 tsp and add it to the dry ingredients, with no proofing.
Less cinnamon: use 1 tbsp instead of 2 1/2 tbsp for a milder roll.
Freezing: freeze the shaped rolls, then thaw, let them do a second rise and bake.