Peel and finely dice the shallots and garlic. Clean and wash broccoli and cauliflower and divide into florets. Dice broccoli and cauliflower stems. Heat the fat in a saucepan and sauté the shallots and garlic. Add broccoli and cauliflower and fry briefly. Deglaze with broth and cook covered for about 15 minutes. After half of the cooking time, lift out some florets with a skimmer.
Tear toast into pieces. Finely mash broccoli and cauliflower in the broth. Stir in crème fraiche and bring the soup briefly to the boil again. Season to taste with salt, pepper and sugar. Put aside the broccoli and cauliflower florets back into the soup and heat it up. Fry bread cubes and hazelnuts in a pan without fat until golden brown. Sprinkle the nut croutons over the soup