In a medium bowl, combine the shredded chicken, ranch dressing, cheddar cheese, mozzarella cheese, red onion, and bell peppers. Mix thoroughly until everything is evenly coated.

Heat a large skillet over medium heat and add 1 tablespoon of butter. Let it melt completely and coat the pan.

Place one tortilla in the hot skillet. Spread half of the chicken mixture evenly over one half of the tortilla.

Fold the empty half of the tortilla over the filling and press down gently. Cook for 2-3 minutes until the bottom is golden brown.

Carefully flip the quesadilla and cook another 2-3 minutes on the other side until the cheese is melted and both sides are golden brown.

Remove from skillet and repeat with remaining tortillas and filling, adding more butter as needed. Cut each quesadilla into three wedges and serve immediately with toppings.