Step 1

In a large pot, combine the beef, star anise, bay, 1 teaspoon salt and 3 quarts water. Bring to a boil over medium-high, then reduce to medium and simmer, uncovered, until a skewer inserted into the meat meets no resistance, 1½ to 2 hours; occasionally skim off and discard the foam that rises to the surface.

Step 2

Meanwhile, in a 12-inch skillet over medium-high, heat 3 tablespoons of the oil until shimmering. Add the onion and ½ teaspoon salt; cook, stirring occasionally, until lightly browned, about 3 minutes. Add half of the beets, the carrots, tomato paste, ½ teaspoon salt and ¾ teaspoon pepper; cook, stirring, until the mixture browns and sticks to the skillet, 3 to 5 minutes.

Step 3

Push the vegetables to the edge of the pan and add the remaining 1 tablespoon oil to the clearing. Add the garlic and caraway; cook, stirring, until fragrant, about 1 minute. Remove the pan from the heat and stir the garlic-caraway mixture into the vegetables. Stir in the tomato puree and paprika, then ladle in 1 cup of the liquid from the large pot. Scrape up any browned bits, then set the skillet aside.

Step 4

When the meat is tender, remove and discard the star anise and bay from the broth. Add the contents of the skillet to the pot, along with the remaining beets and the potatoes. Simmer, uncovered and stirring occasionally, until the potatoes are tender, about 20 minutes.

Step 5

Stir in the cabbage and beans. Cook, stirring occasionally, until the cabbage is tender, 5 to 8 minutes. Off heat, stir in the vinegar. Taste and season with salt, pepper and additional vinegar, if needed. Ladle into bowls, top each with a dollop of sour cream and sprinkle with dill.