Pour 1 cup of water into a soup pot, add the potatoes cut into pieces and boil until done. When the pieces are soft, drain the water and mash the potatoes until they resemble puree.
Pour in the milk, turn on low heat, wait until it boils, add salt and black pepper if desired, cook on low heat for about 5 more minutes. Then add finely chopped cucumbers, cook for no more than 5 minutes. Finely chop a few sprigs of dill, add to the soup, turn off the heat.