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Place beans in a bowl or pot and mix in kosher salt. Add enough cold water to cover the beans, plus an extra 2-3 inches of water. Leave at room temperature to soak 8 – 24 hours.
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In a large Dutch oven or other oven safe pot (at least 6 ¾ quarts, unless you are scaling down the recipe), cook bacon over medium heat until browned, 7-10 minutes, stirring often. Remove bacon with a slotted spoon to a paper-towel lined plate.
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Season pork shoulder pieces and chicken thighs with black pepper. (I do not use salt due to the salt in the bacon and sausage.)
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Turn heat to medium-high. Brown the pork shoulder in the pot with the bacon fat, stirring often to get all sides browned. Remove browned pork to a plate.
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Brown chicken thighs in the pot with the pork fat over medium-high heat, 3-5 minutes per side. Brown in 2 batches if they don’t all fit in a single layer. Remove browned chicken to a plate.
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Cook sausage in the same pot over medium heat, stirring often, until nicely browned. Remove to a plate. Pour out all but 2 tablespoons of fat.
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Add onion, carrots, and celery, and cook for 7 minutes, stirring frequently. Add garlic and cook 3 more minutes. Add tomato paste and stir to mix. Add chicken broth. Scrape up any browned bits from the bottom of the pan.
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Drain beans and rinse under cold water. Add beans to pot with onion. Bring to a simmer. Cover and reduce heat to low. Simmer for 1 hour.
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Meanwhile, preheat oven to 300 degrees.
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When beans have simmered for 1 hour, add sausage, pork, and bacon to the beans and mix to incorporate. Top with thyme sprigs. Place chicken thighs on top of the mixture, skin side up. Cover and transfer to oven.
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Bake for 3 ½ hours. Check the liquid level about halfway through. If the beans are not covered, pour in a little water.
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Let cool for 10 minutes before serving.