In a large soup pot, combine the beef cubes and water (or broth). Bring to a boil, carefully skim off any foam that rises to the top, then reduce heat to low and simmer covered for 45 minutes until the beef is tender.

While the beef simmers, prepare the vegetable base (zazharka). Heat the vegetable oil in a large skillet over medium heat, add the diced onions and grated carrots, and sauté for 5-7 minutes until the onions are translucent.

Add the grated beets, tomato paste, and lemon juice to the skillet with the onions and carrots. Cook for another 10 minutes, stirring occasionally, until the beets soften and the mixture is fragrant.

Add the cubed potatoes to the main pot with the beef and cook for 10-15 minutes until almost tender. Then, add the shredded cabbage and cook for an additional 5 minutes.

Stir the sautéed beet mixture into the soup pot until the broth turns a rich ruby red. Add the minced garlic, salt, and pepper, and simmer gently for 5-10 minutes to blend all the flavors.

Remove the pot from heat and let the borsch rest for at least 15 minutes to allow the flavors to deepen. Ladle into bowls and serve warm, topped with a generous spoonful of sour cream and chopped fresh dill.