Rinse the Brussels sprouts and discard any wilted outer leaves. Peel the potato and cut it into cubes. Peel and chop the onion finely; also peel and slice the garlic.
In a smaller pot, boil the water, salt it properly (about the same as for pasta, so rather more salt). Carefully drop in about a third of the brussels sprouts and cook for 10 minutes. Then drain the water and cover the sprouts with cold water. Later, you will put the heads prepared in this way into the soup.
Quarter the remaining two-thirds of the brussels sprouts.
Heat the lard in a soup pot over medium heat and fry the onions while stirring until pink. Add the quartered cabbage, chopped potato, and garlic. Sauté for about 3-4 minutes, stirring frequently.
Pour in the broth, add salt. Bring the soup to a boil, then turn the heat down to a minimum and cover with a lid. Cook for about 15-20 minutes until the sprouts and potatoes are soft.
Remove the pot from the stove, add the marjoram. Rub it in between your fingers beforehand. Pour in the heavy cream. Finally, blend the soup with an immersion stick blender. Do not boil anymore.
Season with wine vinegar, sugar. Add salt, stir well.
Finally, quarter a third of the sprouts you have previously cooked, and add them to the soup. Before serving, let the sprouts warm up in the soup for a while.