Preheat a grill pan or skillet over medium-high heat.
Brush the flank steak with olive oil and season both sides with salt and black pepper.
Place the steak on the hot pan and cook for 4-5 minutes per side for medium-rare, or until desired doneness is reached.
Remove the steak from the pan and let it rest for 5 minutes, then slice thinly against the grain.
In the same pan, add the butter and sauté the sliced onions over medium heat until soft and caramelized, about 7 minutes.
Toast the sandwich bread slices until golden brown.
Spread mayonnaise on two slices of the toasted bread and Dijon mustard on the other two slices.
Layer the sliced steak evenly over the mayonnaise-spread bread slices.
Top the steak with sautéed onions and a slice of provolone cheese on each sandwich.
Place the sandwiches open-faced back onto the warm pan or under a broiler just until the cheese melts, about 1-2 minutes.
Assemble the sandwiches by placing the mustard-spread bread slices on top of the melted cheese and press gently.
Cut each sandwich in half and serve immediately.