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Add the oil to a large cast iron skillet on medium heat.
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Add the diced onion and minced garlic. Cook for about 3-4 minutes until the onion starts to soften, stirring a few times.
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Add the chicken to the pan and break it apart with a wooden spoon or spatula. Distribute evenly and mix in with the onion. Cook for 10 minutes stirring a few times.
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Add the salt, pepper, cayenne pepper, white vinegar, Worcestershire sauce and hot pepper sauce, stir to combine.
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In a small cup mix the chicken broth and cornstarch together, add the slurry to the pan. Stir to combine and cook for another 5 minutes on low heat or until the mixture is only slightly liquidy.
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Turn off the heat, mix in the shredded cheese.
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Serve on toasted brioche buns.
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Optional: top with diced tomatoes, sour cream and cilantro.
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Store leftovers in an airtight container in the fridge for up to 4-5 days.