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 and the mixture looks creamy.

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

Place one tortilla in the hot skillet. Spread half of the chicken mixture evenly over one half of the tortilla, leaving about 1/2 inch from the edges.

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

Carefully flip the quesadilla using a wide spatula and cook another 2-3 minutes on the other side until the cheese is fully melted and bubbling, 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 your favorite toppings.