In a non-reactive saucepan, cover the chilies with water and simmer 5 minutes. Remove from heat. Let them soak for 5 more minutes, then drain.
Put 1/4 c chicken stock into a blender/food processor with cloves, garlic, cumin. Blend. Season with salt. Add 1 c more stock and 1 chili at a time, blending to a smooth consistency before adding the next. Do this to all the chilies.
Heat the oil in a large saucepan. Add the pasta, keeping the nests intact, and fry it (very strange, yes), turning the nests until they reach a deep golden color. This should only take about 3 minutes. Ours turned a nice crusty brown. Be sure to keep the nests intact. Strain off the oil.
Add the sauce to the pasta. Turn up to moderate heat for about 3 minutes, scraping the bottom to keep the pasta from sticking. Cover. Cook on low, adding the remaining stock a little at a time to prevent sticking. Cook another 5-8 minutes.
Serve one nest per person with wedges of avocado and a wedge of lime. Squeeze a little bit of the lime and some cheese over the nest and eat.