Step 1: Pat the pork chunks dry with paper towels and season generously with salt and pepper. In a large Dutch oven or heavy-bottomed pot, heat olive oil over medium-high heat. Sear the pork in batches until deeply golden brown on all sides, about 3-4 minutes per side. Remove seared pork to a plate and set aside.
Step 2: Reduce heat to medium. Add the chopped onion to the pot and sauté until softened and translucent, about 5-7 minutes, scraping up any browned bits from the bottom. Add the sliced apple and cook for another 3-4 minutes until slightly softened. Stir in the minced garlic and cook for 1 minute until fragrant.
Step 3: Return the seared pork to the pot. Add the drained sauerkraut, bay leaves, caraway seeds (if using), and chicken broth. Stir to combine, ensuring the pork is mostly submerged.
Step 4: Bring the mixture to a gentle simmer, then reduce heat to low, cover tightly, and simmer for 2.5 to 3.5 hours, or until the pork is fall-apart tender. Check periodically to ensure there’s enough liquid; add more broth if needed. Taste and adjust seasonings, adding more salt, pepper, or a pinch of brown sugar to balance the tartness if desired.
Step 5: Remove the bay leaves. Shred the pork directly in the pot or remove, shred, and return to the sauerkraut mixture. Serve hot, garnished with fresh parsley and a dollop of sour cream, if desired.