Preheat the oven to 300°F. Gather and prep all ingredients.
Season the pork butt thoroughly on all sides with salt, pepper, and garlic powder.
Heat oil in a large Dutch oven over medium-high heat. Sear the pork on all sides until deeply golden, about 8-10 minutes total. Transfer pork to a plate.
Reduce the heat to medium. Add the onion and apples to the pot and cook, stirring occasionally, until softened and lightly browned, 5-8 minutes.
Stir in the garlic, brown sugar, Dijon mustard, caraway seeds, smoked paprika, remaining black pepper, and bay leaf. Cook until fragrant, about 1 minute.
Add the sauerkraut and pour in the chicken broth, stirring well to combine and create an even sauerkraut bed.
Nestle the pork butt on top of the sauerkraut mixture. Cover with the lid and transfer to the oven. Roast for 3-3½ hours, or until the pork is fork-tender.
Remove the lid, increase oven temperature to 375°F, and continue roasting for 20-30 minutes, allowing the pork to brown and the liquid to reduce slightly.
Remove from the oven and let rest for 10 minutes. Shred the pork directly in the Dutch oven using two forks, then fold it into the sauerkraut mixture and serve warm.
*Caraway seeds are key to the classic German-inspired flavor of this dish. If unavailable, ¾ teaspoon fennel seed can be substituted, though the flavor will be slightly sweeter and less earthy.**This recipe is tested and cost out using Better Than Bouillon to make the chicken broth. If using a different broth or stock, seasoning levels may vary. Taste before serving and adjust salt as needed.Make-ahead friendly: This dish tastes even better the next day as the flavors meld. Reheat gently on the stovetop or in a low oven.