Clean and wash the cabbage, remove a few leaves and set aside. Cut the rest in half. Peel onion and garlic and chop finely. Heat 2 tablespoons of oil in a large pot. Sauté the onion, garlic and brussels sprouts.
Extinguish with 3⁄4 l water. Stir in stock and bring to the boil. Cover and simmer for about 15 minutes. Meanwhile blanch the Brussels sprouts in boiling salted water for about 2 minutes. Drain, rinse with cold water and let drain.
For the croutons, wash the herbs, shake dry and pluck the leaves. Put the herbs and 100 ml oil into a tall mixing bowl and puree with a hand blender. Season with salt. Cut bread into cubes of about 2 cm.
Melt the butter in a pan. Fry the bread cubes until crispy all around. Add approx. 1⁄3 of the herb oil and toss the croutons briefly in it. Take them off the stove.
Grate cheese. Pour cream into the soup and puree everything finely with a hand blender. Ca. 2⁄3 Add cheese and melt in the hot soup while stirring. Season to taste with salt and pepper. Serve the soup with cabbage leaves, croutons and other cheese.
Drizzle with some herb oil. The rest is enough.