Peel and finely dice the onions and garlic. Peel, wash and cut the potatoes into small pieces.
Heat the butter in a large pot. Sauté onions and garlic in it. Add potatoes and steam briefly. 1 1⁄4 Pour on 1 l water and milk, bring to the boil. Stir in stock. Cover and simmer for about 20 minutes.
In the meantime clean and wash the spring onions and cut them into fine rings. Peel, wash and finely dice the carrots. Clean, wash and finely slice radishes. Halve roast beef slices.
Stir horseradish into the soup and puree everything finely with a hand blender. Add the carrots and continue cooking for about 5 minutes. Add spring onions 1 minute before the end of the cooking time. Season soup with salt, pepper and nutmeg.
Serve with radishes and roast beef.