In a mixing bowl, add the avocados. Using a fork, slightly mash the avocados. Add half of the onion, lime juice jalapeño pepper and garlic. Mix thoroughly.
Season the mixture with salt, pepper and hot sauce to taste. Sprinkle 1/2 of each cheese over the top of two individual tortillas and sprinkle with the drained chiles, remaining onion and cilantro. Top the tortillas with the remaining two tortillas.
Preheat the Emerilware Quesadilla Pan over medium-high heat until hot. Add 1 tablespoon of the oil and, when hot, gently lay a quesadilla in the hot oil and pan-fry for about two minutes, or until golden brown on the bottom.
Using a pastry brush, brush the top of the quesadilla with one teaspoon of the remaining oil then turn and cook on the second side until golden brown, about two minutes longer. Remove the quesadilla from the pan and repeat the cooking process for the remaining quesadilla.
Serve the quesadillas with salsa, sour cream and guacamole.