Divide cheeses in half, and add equal parts of of half the shredded cheeses to one side of each tortilla, set aside.
Add oil to a griddle or large skillet over medium high heat, heating till the oil shimmers. Add onions and sauté until caramelized. Set aside.
Add the meat to the skillet, and cook the steak just enough to warm it. About three minutes total. Remove the meat and reduce heat to medium.
Add the warm meat on top of the cheese, top with onions, bbq sauce and the remaining half of cheese. Fold tortilla in half and place back in the skillet. Move the tortilla around the skillet until the cheese melts and the tortilla gets golden brown. Flip and repeat, about four minutes total.
Remove from the pan, repeat with remaining quesadillas. Serve with a drizzle of sour cream and additional bbq sauce if desired and pickled red onions.