Step 1

Adjust oven rack to lower-middle position and heat oven to 325 degrees. Pat pork dry with paper towels and sprinkle with 1 teaspoon salt and ½ teaspoon pepper.

Step 2

Heat oil in Dutch oven over medium-high heat until just smoking. Add half of pork and cook, stirring occasionally, until brown on all sides, about 8 minutes; transfer to bowl. (Reduce heat if bottom of pot begins to scorch.) Repeat with remaining pork.

Step 3

Reduce heat to medium. Add onion, bell pepper, celery, tomato, and ½ teaspoon salt to now-empty pot and cook until vegetables are softened and liquid has evaporated, 8 to 10 minutes, scraping up any browned bits.

Step 4

Add paprika, caraway seeds, and garlic and cook until fragrant, about 1 minute. Stir in water and pork and any accumulated juices and bring to simmer, scraping up any browned bits. Cover, transfer to oven, and cook for 1 hour. Stir in sauerkraut, cover, return pot to oven, and continue to cook until pork is fully tender, about 30 minutes longer.

Step 5

Using wide spoon, skim off any surface fat. Season with salt and pepper to taste. Serve, garnished with sour cream and dill.