Preheat the oven to 350°F. Lightly grease a 9×13-inch baking dish and set aside.
Using a serrated knife, slice the Hawaiian rolls in half horizontally. The easiest method: We keep all 12 rolls connected and slice the entire package in half horizontally. It is much faster than cutting each roll individually and gets plenty of cinnamon butter into every roll.
In a small bowl, mix together the brown sugar, cinnamon, 8 tablespoons of butter, and ⅛ teaspoon salt until smooth and spreadable.
Spread about ¾ of the cinnamon butter mixture evenly over the bottom halves of the rolls. Place the tops back on, then spread the remaining cinnamon butter over the tops.
Place the rolls in the prepared baking dish and bake for 14-20 minutes, or until warmed through and lightly golden on top.
Let the rolls sit for 5 minutes before frosting.
While the rolls bake, beat together the remaining 1 tablespoon butter, cream cheese, remaining salt, vanilla, and powdered sugar until smooth and creamy.
Spread the icing over the warm rolls, letting it melt into all the nooks and crannies. Serve warm.