Heat the oil in a Dutch oven or large, heavy pot over medium-high heat. Sprinkle the pork with salt and pepper. Working in batches, add the pork in a single layer and cook, turning, until browned on all sides, about 6 minutes. Transfer the pork to a large bowl after each batch. Add the tomatillos and cook until softened and browned, about 4 minutes. Transfer to a clean bowl. Lower the heat to medium and add the garlic and onions and cook, stirring often, until softened, about 3 minutes. Stir the cornmeal into the pot until thickened, then add the chicken broth. Return the pork to the pot and bring to a simmer.
Put the blistered tomatillos, jalapenos, lime juice and half of the cilantro in a blender and blend until smooth. Add the sauce to the pot. Simmer until the pork is tender and the sauce thickens, about 2 1/2 hours.
Serve over rice sprinkled with the remaining cilantro.
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