Turn on your oven broiler. Place the rack 6 inches from the top.

Line a baking sheet with aluminum foil. Place chilies on baking sheet. Broil until skin is blackened and blistered, about 5 - 6 minutes per side. Note you can also do this part on your grill. The cooking time would be more like 3 minutes on each side.

Transfer roasted peppers to a paper bag and close for 15 minutes. This will allow the peppers to sweat making removing the skin easier.

Using gloves, carefully remove the skin, seeds and stems of the roasted peppers. Chop and set aside.

Heat butter and olive oil in a skillet over medium heat. Once butter has melted begin sauteing the onions. Cook until they start to brown, about 15 minutes. Stir in the roasted peppers, garlic and salt. Remove from heat.

To assemble a quesadilla, place one tortilla on a flat surface, sprinkle half the cheese and half of the pepper mixture onto the tortilla. Place the other tortilla on top. Repeat with remaining ingredients. Cook the quesadillas in a non-stick skillet over medium-high heat until the cheese is melted and the tortilla begins to brown. Slice and serve immediately.