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For the hash: Preheat the oven to 300 degrees F. Sprinkle the pork belly generously with salt and black pepper and place in a medium high-sided saute pan with a lid. Add the stock, cilantro sprigs and smashed garlic and bring to a simmer. Cover with the lid and transfer to the oven. Let the pork belly braise until really tender, about 2 hours 30 minutes. Uncover and let it cool to room temperature in the stock. Remove the pork, pat it dry and put it in a large shallow bowl. Cover the bowl with plastic and place another bowl on top with a can of beans or tomatoes to weight it down. Chill for 8 hours and up to 24 hours.
Remove the pork belly from the refrigerator and remove the skin. Cut the pork into 1/2-inch cubes. Toss the cubes in the 2 tablespoons jerk rub. Heat a few tablespoons of canola oil in a large cast-iron skillet over medium heat. Add the pork and cook until golden brown and crispy. Remove the pork with a slotted spoon to a plated lined with paper towels.
Add the onion, red pepper and poblano to the pork drippings in the pan and cook until soft. Add the chopped garlic and cilantro and cook for another minute. Add the sweet potatoes and more oil if needed. Season with salt and black pepper and cook the potatoes, pressing firmly with a spatula, until they are deep golden brown on the bottom. Add the pork, turn the potatoes and cook, pressing with the spatula, to brown the other side of the potatoes and heat the pork.
Heat the butter in a nonstick or cast-iron pan over medium heat. Carefully crack the eggs into the pan and sprinkle with salt and black pepper. Fry until the edges begin to set and the yolk is slightly firm. Flip them over and cook for another minute longer. Or, instead of flipping, cover the eggs with a lid for 1 to 2 minutes to "baste"; the yolk should still be runny. Divide the hash among 4 plates and top each with an egg. Drizzle with hot sauce and garn