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Heat a cast iron skillet over high heat. Once hot, season chicken legs with salt and add them skin-side down to crisp up. Once browned and crispy, remove from skillet and set aside. Use a spatula to scrape up any browned bits stuck to the bottom of the pan.
Add a tablespoon of olive oil to the skillet before adding onion, 2 cloves sliced garlic, and sausage meat. Stir to combine, letting the sausage color the onions and flatten everything down into a base in the pan. Season with salt and add a bit more oil to the pan.
Use your hands to pull the meat and skin off the chicken bones in large chunks. Once the onions have started to crisp and caramelize and the sausage is cooked through, add the chicken to the pan and stir to combine. Remove everything from the pan and set aside, then return the skillet to high heat.
Add another few tablespoons of oil to the pan and let it get piping hot. Add the leftover rice to the pan and pat down into a layer to crisp the bottom of the rice. Add the chicken mixture back to the pan and spread out evenly to cover the rice, patting it down into.
Add 2 tablespoons olive oil to a nonstick skillet along with remaining sliced garlic clove and hot pepper, season lightly with salt. Set the pan over medium heat to let the vegetables soften, then add a few tablespoons of butter.
Add a few dots of butter around the edges of the cast iron skillet to further crisp and caramelize the rice.
Once the butter in the nonstick skillet has melted, crack the eggs into the pan over the garlic and peppers. Reduce the heat to medium low while the eggs cook.
Once egg whites are cooked, top with half the cilantro and add the remaining cilantro on top of the chicken mixture in the other skillet.
Once the butter has melted into the rice, remove the skillet from heat and place a large plate or platter upside down on top of the skillet. Carefully flip the skillet over onto the plate, then gently bang the plate and skillet down on the counter. Give the skillet a few strong taps with tongs or a spatula to ensure the rice releases itself onto the plate. Lift the skillet away and top with the eggs and any remaining garlic and peppers. Serve immediately.