Pork and Kielbasa with Sauerkraut, Mushrooms and Potatoes

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3 pounds fresh (refrigerated) sauerkraut

2 cups chicken or beef broth

1 ounce (1 cup loosely packed) dried mushrooms

1 tablespoon vegetable oil, or more if needed

2 pounds pork shoulder (butt) or loin, cut into 1-inch cubes, well trimmed

1 pound kielbasa

1 teaspoon caraway seeds

2 pounds Yukon Gold potatoes, peeled and cut into 2-inch chunks

3/4 pound parsnips, scrubbed and cut into 2-inch chunks (or use 2 additional potatoes)

1/2 cup sour cream, plus more to pass at the table

Salt and pepper

1/4 cup chopped fresh dill for garnish