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In a large skillet over medium heat, cook chicken until no longer pink in the center, about 5 to 7 minutes per side. Remove from skillet, cool until able to handle, then shred chicken.
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In a same skillet, add cream cheese and 1/4 cup milk. Cook until cream cheese begins to melt, stirring often. Add pepper jack and cheddar cheeses. Once cheeses are melted, add cumin, adobo, oregano, cayenne, salt, and pepper. Stir to combine. Add corn, black beans, and shredded chicken; site to combine.
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If dip seems too thick, add more milk a tablespoon at a time. Add more salt and pepper, if desired, to taste.
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In a large pot (or deep fryer) heat oil over high heat. Fry wontons until golden on both sides. Remove to paper towel lined baking sheet and sprinkle with salt.