Brown the Ground Beef
In a medium Dutch oven or heavy pot, heat the pan over medium-high heat. Add the ground beef and a generous pinch of salt. Spread the beef evenly across the pot, allowing it to sear for 3 minutes. Break the meat into smaller pieces and continue cooking for another 3 minutes, stirring occasionally, until the beef is evenly browned.
Cook the Rice
Stir in the basmati rice, ensuring it gets coated with the beef fat. Cook, stirring frequently, for about 3 minutes, allowing the rice to develop a golden color.
Sauté the Onion
Add the chopped onion to the pot and cook, stirring frequently, for 5 minutes, until the onion softens and becomes translucent.
Season with Paprika and Garlic
Add the sweet paprika and minced garlic, stirring for 1 minute until fragrant.
Add Tomatoes and Sauerkraut
Pour in the canned whole tomatoes, crushing them as you add them to the pot. Add 6 cups of water, sauerkraut, and brine (or fresh cabbage and vinegar, if substituting). Toss in the parsley bunch and a pinch of salt. Bring the mixture to a boil, cover loosely with a lid, and simmer for 15 minutes.
Final Adjustments
Taste and adjust the seasoning with additional salt, if needed. Discard the parsley bunch and serve the soup hot, garnished with freshly chopped parsley.