Peel, rinse and slice the potatoes. In a pot with a thick bottom, heat the olive oil with butter, add potatoes and fry for about 5 minutes so they brown in places. Add peeled and halved garlic and fry together for 2 minutes. Salt the potatoes.
In the meantime, rinse the beet greens thoroughly (beetroots and leaves). Cut the beetroots into thin slices and add to the potatoes. Fry together for about 2 minutes, then add the chopped stems (keep the leaves, we add them at the end of cooking the soup).
Pour wine into the pot with potatoes if using and evaporate it completely. Pour in the broth and bring to a boil. Reduce heat to minimum and cook the soup for about 10-15 minutes until potatoes and beetroots are soft. Near the end, add beet green leaves cut into 1 cm pieces and cook for about 2 minutes. Add 3 tablespoons of chopped dill and remove from heat.
Place the cream in a small cup and thin with a few tablespoons of lukewarm water, then add a tablespoon of soup broth each time, stirring, add about 10 tablespoons of broth this way, only then can we add this tempered cream to the pot with soup. The soup does not need to be cooked anymore. Serve with crumbled feta and the rest of the dill.