Step 1Place the pork pieces in a large bowl and season with 1 teaspoon salt and one-fourth teaspoon pepper, tossing the pork so that it is evenly coated.
Step 2In a 4-quart, heavy-bottom pot, heat the oil over medium-high heat until hot. Add the pork and saute, stirring frequently, until the pieces are browned on all sides, about 15 minutes. This may need to be done in batches. Remove the pork to a bowl and set aside.
Step 3Add the sausage to the pot and saute until the pieces are lightly browned on all sides, 3 to 5 minutes. Strain and set aside with the sauteed pork.
Step 4Add the onions and mushrooms to the pot, along with a little extra oil if needed. Saute the vegetables until the onions are lightly colored, stirring frequently. Stir in the garlic, caraway seeds and paprika and continue to cook, stirring constantly, until the garlic and spices become fragrant, about 1 minute. Stir in the tomato paste, coating the vegetables evenly, and cook for a minute or two until the paste just begins to darken in color.
Step 5Stir in 2 cups broth and increase the heat to high. Cook, stirring the contents of the pot and scraping any flavorings from the bottom of the pot, until the mixture comes to a good simmer. Add the pork and sausage back to the pot, along with the rest of the stock.
Step 6In a medium bowl, combine the flour and water to form a slurry, making sure there are no lumps. Whisk the slurry into the pot, and bring the mixture to a boil. Reduce the heat to a strong simmer and cook until the meat is tender and the pork almost falls apart, about 30 minutes. Stir frequently, making sure to scrape the bottom of the pot so the flour does not burn.
Step 7Stir in the parsley and potatoes and cook until the potatoes are tender but not falling apart, 10 to 15 minutes. This makes about 2 1/2 quarts stew.
Step 8Season to taste with additional salt, pepper and paprika before serving.