In a large deep mixing bowl; add flour, sugar, salt and yeast and using a spoon mix the ingredients until combined.
Whisk eggs and milk together until combined and pour into the flour and sugar mixture, followed by the melted butter and knead into a soft dough,
If the dough is a bit sticky, dust with a little flour and knead until smooth.
Cover with plastic wrap and set aside to rise for between 2-3 hours in a warm place.
After the dough has risen, punch it down to remove any air bubbles and knead it again into a ball.
Roll the dough out into a large rectangle approx 16 inches long by 8 inches wide
Spread the softened butter all over the rectangle EXCEPT the edges on all four sides.
Mix the brown sugar and the cinnamon together and sprinkle all over the rectangle surface. The softened butter will help the mixture to stick
Roll the up the dough by starting at the long side 16 inches approx and rolling into the 8 inches approx. The result should be a long reasonably thick sausage shaped dough. Pinch the edges together to seal; they should stick because there is no butter causing them to slip open.
Cut off the ends to even them out the dough edges and then slice the dough using a sharp and big enough knife into one inch thick slices.
Place the cut slices onto a lined baking sheet about 1 inch apart from each other.
Rub a piece of plastic wrap with a softened butter and cover loosely over the buns and set aside for half-hour to double in size.
Preheat the oven to 200C (180C in a fan oven) or 360F to 400F
Remove the plastic wrap and place the buns in the oven to bake for 15-20 mins.
For the icing:
In a medium mixing bowl, add cream cheese, icing sugar and vanilla extract and mix until smooth and creamy.
Remove the buns from the oven when done and spread the icing over them while still warm, allowing it to drape over them naturally.
Once cooled these buns can be placed in bags or airtight containers and put in the freezer.