Start by cutting the chicken breasts into smaller pieces (3 pieces per breast) and marinating it with the lime juice and some salt and pepper. Cover and refrigerate for at least 30 minutes.
Cooking the chicken using a Pressure cooker:
Add some olive oil to the pressure cooker and sear the chicken on both sides over medium high heat. Add 8 cups of water, season with some salt, close the pressure cooker and once the pressure begins, lower the heat to medium low. Cook for 15 minutes or until the chicken is tender.
Drain the water and close the pan again. Shake 10 times vigorously (it's a good exercise!) or until the chicken is shredded. (** It is important that there's no pressure inside the pan when you shake it! **)
Cooking the chicken on a regular pan:
On a large pot, over medium high heat, heat some olive oil and sear the chicken on all sides. Add 8 cups of water, season with salt and, once it boils, lower the heat to medium low and let the chicken simmer for 20-25 minutes or until it is tender.
Remove chicken from pot and, once is cool, shred it with a fork.
Making the quesadilla filling:
In a large saute pan, heat 2 tablespoons of olive oil and sauté the onion and garlic for a few minutes. Add the peppers and cook until tender.
Add the shredded chicken, the roasted Pasilla chile sauce and the cilantro, if using. Stir everything until combined. Reduce heat to low and let it simmer for 10 minutes.Taste for seasoning and add some more salt if necessary. If desired, add 2 tablespoons of butter to the mixture for creaminess. Stir to combine. Reserve.
Assembling the quesadillas:
Mix both kinds of cheese in a bowl and reserve.
Heat a large skillet over medium heat until hot, about 3 minutes. Add 1/2 a tablespoon of butter and let it melt. Place a tortilla in the pan and sprinkle with 1/4 of the cheese and 1/4 of the chicken. Top with a second tortilla and cook until the bottom tortilla is golden brown and the cheese is starting to melt.
Using a spatula and your hands, carefully flip the quesadilla over and cook until the second tortilla is crisp and golden brown and all the cheese is melted.
Slide the quesadilla to a cutting board and cut into wedges.
Repeat all the steps above with the next 3 quesadillas.
Serve with guacamole, sour cream and/or fresh salsa.