In a bowl, toss the sliced steak with the lime juice, olive oil, and spices. Let it sit for at least 10 minutes. The acidity in the lime helps tenderize the fibers of the flank steak quickly.
Heat a cast-iron skillet over high heat. Add the steak in a single layer (work in batches if necessary). Sear for 2 minutes per side until charred and just cooked through. Remove the meat and let it rest; this keeps the juices inside the steak rather than soaking the tortilla.
In the same skillet, sauté the peppers and onions until they have softened and developed dark, charred edges.
Wipe the skillet clean and reduce heat to medium. Lightly butter one side of a tortilla. Sprinkle a tablespoon of Grated Parmesan directly onto the hot skillet and place the buttered side of the tortilla on top of the cheese. This creates a crispy, salty "frico" crust on the outside.
On one half of the tortilla, layer the shredded Mexican cheese, the seared steak, and the charred vegetables. Fold the other half over.
Cook for 2-3 minutes per side until the tortilla is golden brown and the cheese inside is fully melted.
Use a pizza cutter to slice the quesadillas into triangles. This prevents the filling from being squeezed out, which often happens with a standard knife.