Place steak and marinade into a large zip-lock bag. Allow to marinate at room temp for 30 minutes.
Meanwhile – Lightly butter one side of each tortilla; set aside.
Slice and sauté pepper and onion until softened (5 – 6 minutes); set aside.
Heat grill to high heat. (I like to use the outdoor grill but this will work just fine done in a grill pan on the stovetop.)
Remove steak from marinade and allow excess to drip off. With paper towels, wipe away marinade from one side, leaving the marinade on the second side. Lay steaks on platter, wiped side up, and spray with oil lightly.*
Lay oiled side down on grill (or grill pan) and cook about 3 - 4 minutes; turn steak over to grill the other side for another 3 minutes, for medium rare.
Remove steak and cover lightly with foil and let rest for 10 minutes. Slice into thin strips.
Place a large non-stick griddle pan over medium heat. Place a tortilla on griddle, buttered side down; add layers of ½ cup cheese, steak strips, bell pepper and onion strips. Top with another ½ cup cheese then place another tortilla on top, buttered side facing up. Cook until golden brown on bottom, flip over to cook the other side. (Do this very carefully to keep filling from falling out).
Continue to cook until the second side is browned, and cheese has melted. (A Panini baker works well for this, if you happen to have one, once the cheese has melted on both sides, it acts as the “glue” to hold it all together.)
Remove and continue cooking second quesadilla. Cut each quesadilla into 4 pieces. (I use a large pizza cutter for this.)
*If the marinade is left on the first side of the steak, it is likely to char before the 4 minutes are up. This is the primary cooking time; it’s okay if the marinade is left to caramelize while grilling for the additional 3 minutes to add more flavor.