Grate the zucchini on a grater, season with salt and put in a colander. Allow to drain for about 30 minutes and wring out vigorously through a cloth so that as much of the liquid is removed as possible.
In the broth, cook the peeled garlic cloves until soft for about 10-15 minutes. At the same time, in another pan, steam the zucchini with a little oil until soft.
Put the drained garlic cloves and zucchini in a bowl and let cool. Add the basil, chilli and 1-2 tablespoon garlic stock and puree with a hand blender. Mix in the green pepper and if the mixture is still too thick, thin it with a little garlic stock. Then fold in the crème fraîche with the mixer. Season everything again to taste.