Heat the vegetable oil in a large pot over medium-high heat until shimmering. Add the pork chunks and sear them on all sides for about 3-4 minutes, stirring occasionally, until they develop a golden-brown crust. This browning creates deeper flavor through the Maillard reaction. Pour in the water and add the bay leaves, then bring to a boil. Once boiling, reduce heat to medium-low and simmer gently for 20-25 minutes until the pork is completely cooked through and tender. I find that searing the meat first creates a much richer, more savory broth than just boiling it plain.
While the pork simmers, prepare all your vegetables: dice the onion into 1/2-inch pieces, dice the celery into 1/2-inch pieces, cut the potatoes into 3/4-inch cubes, and mince the garlic. Having everything prepped and ready (mise en place) makes the next steps smooth and prevents overcooking any single component. Rinse and drain the sauerkraut, squeezing gently to remove excess liquid—this helps control the tanginess of the final soup.
Once the pork is tender, add the minced garlic, diced onion, diced celery, and ground cumin to the pot. Stir well and cook for 2-3 minutes, allowing the aromatics to bloom and release their flavors into the broth. The cumin will become fragrant and add a subtle warmth to the soup. I like to add the cumin at this point rather than at the end because gentle simmering allows its flavors to mellow and integrate beautifully with the broth.
Add the potato cubes and drained sauerkraut to the pot, stirring to combine. Season with sea salt and black pepper to taste. Bring the soup back to a gentle boil, then reduce heat to medium-low and simmer for 15-18 minutes until the potatoes are tender but still hold their shape. The sauerkraut will continue to soften and its tangy flavor will marry with the savory broth and spices.
Taste the soup and adjust seasoning as needed—you may want a touch more salt or a grind of fresh pepper depending on your preference. Remove the bay leaves before serving. Ladle into bowls and serve hot. The soup is ready to enjoy immediately, though it actually tastes even better the next day as the flavors continue to deepen.