Cook thinly sliced steak in skillet on medium-high until nicely browned and forming bits of char. Season with salt and pepper.
Melt one tablespoon of butter in a skillet and saute green peppers till beginning to soften, then saute onions. (These can be sauteed together, however green onions cook slower, so start them first)
While vegetables saute, lightly toast bread to firm it up. Toasted bread should still be pale in color.
Divide beef, onions, and peppers into 6 equal portions for 6 sandwiches.
Liberally butter one side of each slice of bread, place buttered side down, top bread with 1 slice of cheese, 1 serving of cooked steak, 1 serving of onion, and 1 serving of peppers. Then top with a second slice of cheese and cover with a second piece of bread, buttered side up.
Working in batches as needed, place sandwich in a clean skillet on medium-low heat and grill until bread is crispy and golden brown and cheese has melted. Adjust heat as needed.
Serve immediately.