In a large bowl, dissolve yeast in warm milk. Add sugar and 1 cup of flour. Stir gently, cover and set aside until doubled in size, about 30-45 minutes.
Add butter, salt, eggs and remaining flour. Mix well with wooden spoon.
Turn dough onto a lightly floured surface and knead for 5 minutes (dough will be a little sticky) Place back in the bowl and cover to let rise until doubled in size.
While dough is rising, make the filling by combining brown sugar, cinnamon and flour in a small bowl.
Roll out onto a 21x16 rectangle, about ¼ inch thick.
Spread the ⅓ cup softened butter then sprinkle with the cinnamon mixture. Roll up long ways and cut into 1¾ inch slices. You should get about 12 cinnamon rolls.
Place on a greased jelly roll pan and let double in size.
Bake at 375 for 15-20 minutes.
While rolls are baking, mix all icing ingredients together. and spread over warm rolls.