Preheat a grill pan or skillet over medium-high heat.
Rub the flank steak with olive oil, salt, and black pepper.
Place the steak on the hot pan and cook for 4-5 minutes on each side for medium-rare, or until desired doneness. Remove from heat and let rest for 5 minutes.
While the steak rests, melt butter in a small skillet over medium heat.
Add the sliced onions and cook, stirring occasionally, until caramelized and golden brown, about 7-8 minutes.
Slice the rested steak thinly against the grain.
Toast the sandwich bread slices until lightly golden.
Spread mayonnaise evenly on one side of each bread slice.
Layer one slice of bread with romaine lettuce leaves, sliced steak, caramelized onions, and a slice of cheddar cheese.
Top with the second slice of bread, mayonnaise side down.
If desired, place the assembled sandwich back on the grill pan for 1-2 minutes to slightly melt the cheese.
Remove from heat, slice the sandwich in half, and serve immediately.