Heat the oil in a large skillet over medium heat. Add the onion and salt; cook, stirring occasionally, for 15-20 minutes, or until the onions are soft and golden brown. Transfer the onions to a dish and wipe the skillet clean.
Add the bean and barbecue sauce to a small bowl and mash lightly with a fork.
Spread the beans over one tortilla. Top with the onions and cover with cheese. Top with the second tortilla.
Transfer the quesadilla to the skillet and cook over medium-high heat for 3-4 minutes on each side, or until golden brown and crisp.
Cut into 4 wedges and serve immediately.