Heat the oil to 350 degrees F in a tabletop deep-fryer or in a Dutch oven with a deep-fry thermometer attached. Place a wire rack over a sheet pan for draining. Fry the tortillas in small batches until crisped and golden, 4 to 6 minutes. Place on the rack to drain.
Spoon the Black Bean Puree over the bottom of a large oval platter. Arrange the fried tortillas over the top. Spoon the Picked Jerk Chicken over top. Top with pineapple, crema, Cotija, avocado and pickled chiles. Garnish with cilantro.
Black Bean Puree:
Heat a 3-quart saucepan over medium heat. Add the oil, onions, jalapeno, coriander and cumin. Cook, stirring frequently, until the onion is soft, 4 to 6 minutes. Stir in the beans. Add the stock, crema and salt to taste. Bring to a simmer. Transfer the mixture to a blender and puree. Yield: about 4 cups.
Picked Jerk Chicken:
Heat the oil in a large skillet over medium-high heat. Add the shredded chicken, soy sauce, jerk paste and stock. Cook for about 3 minutes and set aside. Yield: 2 cups.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.