Mix all ingredients (except tortillas, cheese, avocados, and cilantro) together in a large, heavy saucepan. Bring to a boil over medium-high heat, stirring frequently. Reduce heat to medium-low, cover and simmer for 30 to 45 minutes, stirring occasionally. Shred the pork, using 2 forks, or mashing with a potato masher. Put shredded pork back into sauce and mix ingredients. Cover up and cook on low for another 10 to 15 minutes.
In a large skillet over medium heat, cook a tortilla about 2 minutes on each side. Spoon some pork onto the tortilla and top with 4 to 5 avocado pieces and cilantro. Heat up another tortilla until toasted and add cheese. Cook until cheese is melted. Place the second tortilla cheese side down on top of the pork and avocado. Cut into 4 slices and repeat process. Garnish with cilantro and serve.