Warm the oil in a large pot over medium-high heat.
Brown the beef in batches until deeply seared. Transfer to a plate.
Soften the onion in the pot. Stir in garlic and tomato paste; cook until brick red.
Return beef to the pot. Pour in broth; add crushed bay, salt, and pepper.
Bring to a simmer. Cover and cook gently for 45 minutes.
Stir in grated beets and carrots. Simmer uncovered for 20 minutes.
Add potatoes, cabbage, and diced tomatoes. Cook until vegetables are tender, 20–25 minutes.
Balance with vinegar and sugar. Adjust salt and pepper. Stir in chopped dill.
Let the soup rest off heat for 10 minutes. Ladle into bowls and add sour cream.