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Heat 2 teaspoons of the oil in a large saucepan over medium heat-high. Add chicken pieces and brown, about 5 minutes. Remove from the pot and onto a plate. Set aside.
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Add remaining teaspoon of oil. Stir in the onion and celery, cook until tender, about 5 to 7 minutes.
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Add in the garlic, jalapeño, green chile peppers, cumin, oregano, salt, cloves, and cayenne. Continue to cook and stir the mixture until tender, about 2 minutes. Mix in the white beans and broth. Bring to a boil. Turn down heat to a simmer and add in the cooked chicken pieces. Continue to simmer, partially covered for 20 minutes.
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Remove chicken pieces from the pot and shred into large chunks, pulling all chicken off the bones. Add in cilantro. Using a potato masher or immersion blender, mash/puree about 1/3 of the soup to provide a thicker consistency.
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Return pulled chicken to the pot and stir in cilantro. Ladle into bowls and serve with a dollop of lime crèma, chopped green onion and hot sauce, if you like.