Sauté onion in 1 Tbl. butter until golden brown, about 7-10 minutes. Season with salt to taste.
Butter sliced sub rolls and broil until lightly toasted.
Bring au just to a boil, then remove from heat. Submerge sliced roast beef in au jus for 5 minutes.
Layer roast beef on toasted sub rolls. Top with caramelized onions and sliced cheese.
Serve with hot au jus for dipping.