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Heat 1 tablespoon oil in a large skillet over medium heat. Add
onions and brown sugar and cook, stirring often, until the onions
are very tender and golden brown, about 15 minutes. Add broth,
vinegar and 1/4 teaspoon salt and cook, stirring, until the liquid
has almost evaporated, 3 to 4 minutes more. Transfer the onions to
a bowl; cover to keep warm. Clean and dry the pan.
Sprinkle the remaining 1/4 teaspoon salt and pepper on both sides
of each steak. Heat the remaining 1 tablespoon oil in the pan over
medium-high heat. Add the steaks and cook until browned, 3 to 5
minutes. Turn them over and top with cheese. Reduce heat to
medium-low, cover and cook until the cheese is melted and the
steaks are cooked to desired doneness, 3 to 5 minutes for medium-
rare. Serve the steaks with the caramelized onions.
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