The night before, place the dried hominy (mote) in a large bowl and cover with cold water by 3 inches; in a separate bowl, rinse the black chuño in several changes of cold water, then cover with fresh water. Soak both 8–12 hours.
Drain the hominy, transfer to a pot, and cover with fresh water by 2 inches. Bring to a boil, then simmer until the kernels are tender and beginning to bloom, 1.5–2 hours; drain and keep warm. Drain the chuño, rinse again, then simmer in fresh water until tender and slightly translucent inside, 45–60 minutes; drain, peel any loose skins, and keep warm.
Place the pork shoulder and bay leaves in a large pot and add about 8 cups of the water to cover. Bring to a boil, skim any foam, reduce to a gentle simmer, and cook until the pork is very tender but holds its shape, 1.5–2 hours.
While the pork cooks, stem and seed the dried ajĂ amarillo chiles and dried ajĂ colorado (ajĂ panca) chiles. Cover with hot water and soak until pliable, about 20 minutes; reserve 1 cup of the soaking liquid and drain the rest.
In a blender, combine the soaked chiles, garlic cloves, stale white bread, ground cumin, dried oregano, 0.5 cup pork cooking broth, and 0.5 cup reserved chile soaking liquid. Blend until very smooth, 1–2 minutes.
Return the pork to the pot with the fried chile sauce and add 2 cups of the reserved pork broth. Simmer gently, stirring occasionally, until the sauce coats the meat and the oil rises to the surface, 20–30 minutes; season with the kosher salt and black pepper.
Serve the fricase hot in bowls with plenty of sauce, accompanied by the cooked hominy and black chuño on the side.