Trim any excessive fat and cut the Pork Shoulder into 2-inch chunks; season lightly with Salt and freshly ground Black Pepper.
Dice the Smoked Bacon and finely chop the Onion and Garlic; core and dice the Tart Apple.
Heat the Pork Lard in a heavy Dutch oven over medium-high heat. Add the bacon and cook until golden and the fat is rendered, then transfer the bacon to a plate, leaving the fat in the pot.
Working in batches so you don’t crowd the pan, brown the pork chunks in the hot fat until well-seared on all sides; transfer the browned pork to the plate with the bacon.
Add the onion and garlic to the pot and sauté until softened and translucent, about 4–5 minutes.
Stir in the diced apple and cook for 1–2 minutes, then add the Sauerkraut (if you prefer a milder tang, rinse and drain it briefly) and mix everything together.
Return the pork and bacon to the pot, then sprinkle in the Caraway Seeds, Sweet Paprika, a few Bay Leaves, and a pinch of Allspice; stir gently to combine.
Pour in enough Pork Stock to come about two-thirds up the meat, bring to a gentle simmer, then reduce the heat to low. Cover and braise gently for 1½–2 hours, or until the pork is fork-tender and flavors are melded.
Taste and adjust seasoning with more Salt and Black Pepper as needed. Remove and discard the Bay Leaves and any whole Allspice before serving.
Ladle the sauerkraut and pork onto plates and serve hot with mashed potatoes or hearty bread to soak up the flavorful pan juices.
