In a large mixing bowl, combine the softened cream cheese, buffalo wing sauce, ranch or blue cheese dressing, cheddar cheese, blue cheese crumbles (if using), garlic powder, and black pepper. Mix until well combined and smooth.

Add the shredded cooked chicken breast to the mixture. Fold gently until the chicken is evenly coated with the buffalo dip mixture.

Heat a large skillet or griddle over medium heat. Lightly brush or spray with olive oil or butter.

Place one flour tortilla in the hot skillet. Sprinkle about 1/4 cup of the shredded Monterey Jack cheese evenly over half of the tortilla.

Spoon approximately 1/2 cup of the buffalo chicken dip mixture over the cheese on the same half of the tortilla.

Sprinkle another 1/4 cup of Monterey Jack cheese over the buffalo chicken dip mixture.

Fold the empty half of the tortilla over the filling to create a half-moon shape.

Cook for 3-5 minutes per side, or until the tortilla is golden brown and crispy, and the cheese is fully melted and gooey. You may need to press down gently with a spatula to ensure even cooking and melting.

Remove the cooked quesadilla from the skillet and place it on a cutting board. Repeat with the remaining tortillas and filling.

Once all quesadillas are cooked, cut each into 2-3 wedges. Serve immediately with extra ranch or blue cheese dressing, chopped green onions, or celery sticks, if desired.