Rinse the Brussel sprouts and remove any wilted outer leaves. Using a sharp knife, peel the potato and cut it into cubes. Peel and chop the onion finely; also peel and slice the garlic.
Blanching sprouts: In a large pot, boil the water, and 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 heads.
Heat the fat in a large saucepan or a soup pot over medium-high heat and saute onion while stirring until lightly golden brown. Add the quartered sprouts, chopped potato, and garlic. Sauté for about 3-4 minutes, stirring frequently.
Pour in the broth, and 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, and add dried marjoram. Rub it in between your fingers beforehand (1). Pour in the heavy cream (2). Finally, blend the soup with an immersion blender (3). Do not boil anymore.
Season with wine vinegar, sugar, or salt if needed. Stir well.
Finally, quarter a third of the sprouts you have previously cooked, and add them to the soup. Before serving, let these sprouts warm up in the soup for a while.