In a blender, combine the marinade ingredients and blend until smooth. Place the chicken in a medium bowl, pour the marinade over it, cover, and refrigerate for 4 hours.
Heat oil in a medium saucepan over medium-high heat. Add the onions and cook until soft and caramelized, about 20 to 25 minutes. Add the balsamic vinegar and cilantro and cook for 5 minutes. Season with salt and pepper, to taste. Set aside.
Preheat grill pan. Brush eggplant with oil on both sides and season with salt and pepper to taste. Grill for 2 minutes on each side. Remove and coarsely chop.
Preheat grill pan over high heat. Remove chicken from marinade and season with salt and pepper to taste. Grill for 4 to 5 minutes on each side until cooked through. Let rest for 5 minutes and slice thinly on the bias. Set aside.
Preheat oven to 450 degrees F.
Place 6 tortillas on a large un-greased baking sheet. Divide the cheese, chicken, onions, and eggplant among the 6 tortillas and season with salt and pepper, to taste.
Stack the tortillas to make three 2 layer tortillas and top with the remaining 3 tortillas. Brush the tops with olive oil and sprinkle with ancho chile powder. Bake for 8 to 12 minutes, or until the tortillas are slightly crisp and the cheese has melted. Cut into quarters and garnish with the Mixed Tomato Salsa.
Mixed Tomato Salsa:
Combine all ingredients in a medium bowl and season with salt and pepper, to taste.