Rinse the Brussels sprouts and remove any wilted outer leaves. Peel the potato and cut it into cubes using a sharp knife. Finely chop the onion and slice the garlic after peeling.
Blanching Brussel sprouts: In a large pot, bring water to a boil and salt it generously, similar to how you would for pasta. Carefully add about a third of the Brussels sprouts and cook for 10 minutes. Then, drain the water and cover the sprouts with cold water. You will add these blanched sprouts to the soup later.
Quarter the remaining two-thirds of the Brussels sprouts.
Heat the fat in a large saucepan or soup pot over medium-high heat. Sauté the onion, stirring until it becomes lightly golden brown. Add the quartered Brussels sprouts, chopped potato, and garlic. Continue to sauté for about 3-4 minutes, stirring frequently.
Pour in the broth and add salt. Bring the soup to a boil, then reduce the heat to low and cover with a lid. Cook for about 15-20 minutes, until the Brussels sprouts and potatoes are soft.
Remove the pot from the stove and add dried marjoram, rubbing it between your fingers first. Pour in the heavy cream, then blend the soup with an immersion blender until smooth. Do not boil the soup anymore.
Season with wine vinegar, sugar, or additional salt if needed. Stir well to combine.
Finally, quarter the third of the sprouts you previously cooked and add them to the soup. Let these sprouts warm up in the soup for a while before serving.