In a large pot, place chicken breasts and add enough water to completely cover them. Bring pot to a boil, cover it, and reduce to a simmer. Let chicken simmer for about 10-14 minutes or just until no longer pink (if it’s still a tiny bit pink at this point, that’s ok- you’ll continue cooking it).
At this point, remove chicken and let it rest for about 10 minutes before shredding it with two forks (or the meat shredder you see below). Add shredded chicken to a pan with some olive oil and the cayenne pepper, cumin, and salt/pepper. Cook on medium heat until chicken is completely cooked through (no longer any pinand spices are mixed in. Set aside
Meanwhile in a smaller pot, saute garlic with half of the onion in olive oil until golden. At this point, add oregano, beans, and about 3 tbsp water (to reach desired consistencand simmer. After about 5 minutes, mash the beans using a potato masher (or anything realluntil it reaches desired smoothness.
In a large baking dish, arrange half of the chips and sprinkle over half of the cheese. Broil for about 3 minutes or until cheese is fully melted. Remove from oven and add chicken and remaining cheese. Broil for another ~3 minutes or until cheese is melted and chicken starts to brown.
Remove from oven and add remaining toppings sequentially (including the other half of the onion), saving the sour cream and cilantro for last.