Step 1: In a medium bowl, combine the shredded chicken and barbecue sauce. Stir until every strand of chicken is evenly coated. Taste, then season with a pinch of salt and a few grinds of black pepper—remember that your barbecue sauce may already contain salt, so adjust sparingly.
Step 2: In a separate bowl, toss together the shredded cheddar, Monterey Jack, diced red onion, minced jalapeño (if using), and chopped cilantro. Mix gently to distribute the onion and jalapeño bits throughout the cheese; these little bursts of flavor will punctuate every bite.
Step 3: Place a large nonstick or cast-iron skillet over medium heat. Brush the surface lightly with olive oil or melted butter—this fat helps the tortilla crisp to a deep golden brown without sticking. Allow the skillet to warm for about a minute; it should feel hot to the touch but not smoking.
Step 4: Lay one flour tortilla flat in the preheated skillet. Evenly sprinkle a quarter of the cheese–onion–cilantro mixture over half of the tortilla. Top the cheese layer with a generous portion of the BBQ chicken, then finish with a light sprinkle of cheese to help seal the fold.
Step 5: Fold the empty half of the tortilla over the filling to form a half-moon. Press down gently with a spatula and cook for 2–3 minutes, or until the underside is deep golden brown and you see melted cheese at the edges.
Step 6: Carefully flip the quesadilla using a wide spatula. Cook the second side for another 2–3 minutes, pressing gently, until both sides are evenly crisp and the cheese is fully melted.
Step 7: Transfer the cooked quesadilla to a warm plate or sheet pan, cover loosely with foil, and wipe the skillet clean if there’s any residue. Re-oil the surface and repeat Steps 4–6 with the remaining tortillas and filling.
Step 8: Let each quesadilla rest for one minute—this allows the cheese to firm up slightly, making slicing cleaner. Using a sharp knife or pizza cutter, cut each half-moon into four wedges. Arrange on a serving platter.
Step 9: Offer bowls of sour cream, extra barbecue sauce, and pico de gallo alongside the quesadilla wedges. A sprinkle of additional cilantro or a dusting of smoked paprika lends a finishing touch.