Lay a piece of aluminum foil measuring 9 inches by 11 inches on a flat work surface. Place half of the ti or banana leaves on top of the foil, and the turkey on top of the leaves. Sprinkle with the salt and liquid smoke. Place the remaining leaves on top of and around the turkey. Cover with additional foil and seal tightly. Place the package in a large roasting pan, fill with 2 inches of water, and cover the pan with foil to seal in the steam.
Cook for 1-1/2 to 2 hours, or until fork tender. When cool, remove the turkey meat and shred using 2 forks. Refrigerate for up to 5 days (or freeze) until needed.
To prepare the quesadillas, in a saute' pan or skillet over medium-high heat, melt the butter. Add the mushrooms and saute' for about 3 minutes, or until golden brown. Spread 1/2 tablespoon of the cheese on one side of each tortilla. Place about 1/4 cup of the turkey evenly over the cheese on 1 of the tortillas. sprinkle 2 tablespoons of the cooked mushrooms over the turkey and top with another tortilla, cheese side down. Keep warm while preparing the remaining 3 quesadillas.
In a medium nonstick pan over medium heat, warm each quesadilla for 2 minutes on each side, or until the tortillas are slightly brown on the outside and hot inside. Cut into eights.
To serve, divide the quesadilla pieces among individual plates. Top with the relish and sour cream. Garnish with the cilantro.