In a mixing bowl, combine the cooked chicken breast with your favorite barbecue sauce. Toss until the chicken is thoroughly coated; this should take about 1-2 minutes. Set aside your savory BBQ chicken mixture.

On a clean surface, lay out two flour tortillas. Evenly sprinkle half of the shredded cheddar and mozzarella cheeses on each tortilla.

Layer the prepared BBQ chicken mixture evenly over the cheese on each tortilla. Then add thinly sliced red onions and fresh cilantro.

Place the remaining tortillas on top of the filled ones, gently pressing down to secure everything. Ensure they are well-sealed.

Heat a large skillet over medium heat and drizzle with olive oil. Carefully place the quesadillas in the skillet, cooking for 3-4 minutes until golden and crispy.

Flip each quesadilla using a spatula, adding another drizzle of olive oil if needed. Cook the second side for another 3-4 minutes until golden brown and cheese is melted.

Once cooked, remove the quesadillas from the skillet and allow to rest for 1-2 minutes before slicing into wedges.

Serve warm, accompanied by sour cream and salsa for extra flavor.