Dissolve the ground saffron in 1/2 tablespoon hot water. Set aside.
Thinly slice the onion and crush the garlic. Cut the chicken into about 1 inch pieces. In a large pot or dutch oven, heat 1 1/2 tablespoons oil over medium high heat. Once heated, add the onion, garlic, and chicken. Cook until browned.
Stir in 1/2 cup water, cover, and simmer over low heat for 45 minutes. Stir occasionally.
Heat a large skillet over medium heat with the remaining 1 1/2 tablespoons oil. Cut off the stems to the mushrooms and slice. Add them to the skillet and sprinkle with flour and parsley. Saute until lightly browned.
Add the sauteed mushrooms, soaked saffron, and lime juice to the chicken mixture. Continue to simmer, covered, for 35 minutes. Stir in the egg yolk and cumin. Simmer for another 5 minutes. Serve hot, garnished with parsley and lime wedges.