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Heat the oil in a large saucepan over medium-low heat.
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Slowly cook and stir the onion until tender.
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Mix in the garlic, jalapeno, green chile peppers, cumin, oregano and cayenne.
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Continue to cook and stir the mixture until tender, about 3 minutes.
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Mix in the chicken broth, turkey or chicken and white beans.
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Simmer 15 minutes, stirring occasionally.
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Remove the mixture from heat; slowly stir in the cheese until melted.