Whisk together the lukewarm water with the instant yeast and 1 tsp of sugar in a medium bowl and let it rest for 5 minutes.
Add eggs, lukewarm milk, sugar and melted butter to the yeast mixture and whisk until well combined.
Combine the flour with the salt and whisk together in a large bowl.
Pour the yeast mixture into the flour mixture and using a wooden spoon stir until well incorporated.
Cover with plastic wrap and let it rest for 10 minutes.
Preheat your oven to 350 F degrees.
Line a 9x13 inch baking pan with parchment paper.
Spray with no-stick spray to keep the parchment paper in tact.
Roll the dough out onto a well floured surface, until it's approximately 16 inches long by 12 inches wide rectangle and about 1/4 inch in thickness.
In a small bowl whisk together the brown sugar with the cinnamon.
Spread the 1/2 cup of softened butter over the entire surface of the dough with the back of a spoon and then sprinkle with the cinnamon sugar evenly over the surface of the dough.
Starting at the long edge, roll the dough down to the bottom edge starting away from you and working in.
Cut the dough into 2 inch slices or use floss and cut through the dough to get 12 rolls.
Place the rolls into the prepared baking pan.
Let the rolls rest for another 10 minutes to let them rise a little more.
Place the baking pan in the oven and bake for 20 minutes or until golden brown.
While the rolls are baking make, prepare the cream cheese icing.
Add the cream cheese and butter to a mixing bowl and mix until smooth. Add the remaining ingredients and mix until smooth. If the icing is a bit too stiff add 1 tbsp of milk.
Ice the rolls immediately when they come out of the oven with the cream cheese icing.