Fry the potatoes on olive oil or butter in a wide and large pot (for about 5 minutes).
Add the peeled and diced onion and the peeled and grated carrot. Stirring occasionally, fry for about 2 minutes. At the end, add garlic pressed through a garlic press.
Pour in broth and bring to a boil. Cook for about 5 minutes.
Cut the beet green leaves from the beets, rinse everything thoroughly. Peel the beets and cut into thin slices or half-slices (you can also grate them on the large holes of a grater).
Add the beets to the broth and cook for about 4 minutes, then add the finely chopped beet green leaves and cook for another 4 minutes, or until the vegetables are tender.
Season with ground pepper and - if needed - salt.
Add lemon juice, cream, and chopped dill.
Serve the soup with hard-boiled egg, cut in half or diced into larger pieces.