In a small saucepan or in a microwave safe measuring cup, melt butter with milk. Add the honey and set aside.
In a large mixing bowl or the bowl of a stand mixer, combine flour, yeast, salt, egg replacer mixture. Add the milk mixture. Mix and knead (use a dough hook on the stand mixer) to form a smooth dough.
Add more flour as needed if the dough is too sticky. It is always better to have a slightly sticky dough than too dry. Takes about 10 mins by hand and 6~8 minutes with the stand mixer. Transfer the dough into a lightly greased bowl.
Cover properly and put in the fridge to make the rolls the next day.*
In the morning, remove the bowl from the fridge and set aside for 1 hour to rise or until the dough is noticeably puffy but not quite doubled in volume.
In a small bowl, combine ground cinnamon and light brown sugar.
Remove the dough from the bowl onto a well floured surface. Gently deflate it and shape into a 12"x18" rectangle.
Brush dough with melted butter. Sprinkle generously with cinnamon mixture. Starting with the long edge, roll the dough into an 18" log. Cut the dough using a serrated bread knife into 16 equal parts - easiest way to do that is by halving the log, then make quarters and so on.
Put the cut rolls in a 9" baking pan - cover and set aside for another 1 hour until puffy.
Preheat the oven to 350°F. Bake the rolls until lightly golden on top and feel set.
While the rolls are baking mix the ingredients for the icing, adding just enough milk/ cream to make a thick spreadable icing. It should thick like very thick cream.
Remove the rolls from the oven, turn them out onto a wire rack. Spread them with the icing.
Serve the rolls warm. Let the leftovers cool completely before storing in an airtight container for up to 3 days. They can be frozen for up to a month.