In a nonreactive medium saucepan, cover the chiles with water and simmer for 5 minutes.
Remove from the heat and let soak until soft, 5 more minutes.
Drain, setting aside 1/2 cup of the chile liquid.
Pour 1/4 cup of the chicken stock into a blender, add the cloves, garlic and cumin seeds and blend until smooth.
Season with salt.
Add 1/2 cup more of the stock, the 1/2 cup chile liquid and the drained chiles, a few at a time, and blend until smooth.
Add more stock if necessary.
Heat the oil in a large heavy saucepan.
Add the pasta and fry turning until it has turned a deep golden color, about 3 minutes (keep nests intact).
Strain off excess oil.
Add the blended sauce to the pasta in the skillet and fry over moderate heat for about 3 minutes, scraping the bottom of the pan to prevent sticking.
Cover and cook over low heat, adding the remaining stock a little at a time to prevent sticking, until the pasta is just cooked through, 5 to 8 minutes.
Transfer to a serving dish and sprinkle with the cheese and green onion slices.