Cover chiles with about 4 cups boiling water and steep until soft, about 15 minutes. Reserve 2 cups soaking liquid and then drain chiles. In a blender, purée chiles with reserved liquid.
Meanwhile, toast the cumin seeds in a dry pan over medium heat until fragrant, then grind them. Toast the fresh oregano (if using dried oregano, don't toast).
Put the beans in a stockpot and cover them with 7 cups water. Add the chile purée, toasted ground cumin, toasted (or dried) oregano, onions, carrots, garlic, jalapeños and chicken thighs. Bring to a boil, reduce heat and simmer, skimming any foam. Remove chicken thighs when cooked, 25 to 30 minutes.
When chicken is cool enough to handle, pull meat from the bones into large pieces and set aside; discard bones. Continue cooking beans until tender, another 1 to 11/2 hours.
Return chicken to pot to heat it thoroughly. Season with salt to taste. Serve in bowls topped with the grated cheese.