Mince the half onion and chop the garlic finely. Rinse the zucchini, trim the ends, and cut the rest into large chunks. Already flake the smoked trout with a fork into small pieces and set aside.
Heat a little oil or butter in a large soup pot. Sauté the minced onion and garlic over medium-high heat until translucent. Add the zucchini chunks and cook for a few minutes, stirring. Pour the five hundred milliliters of broth into the pan and bring to a boil. Lower the heat and let the soup simmer gently for about ten minutes until the zucchini is completely soft and cooked through.
Remove the pan from the heat. Blend the warm mixture with an immersion blender until smooth and even with no remaining pieces. Season with salt and pepper if needed.
Ladle the hot zucchini soup into deep bowls or soup cups. Garnish each portion by distributing the reserved smoked trout flakes over the soup. Serve immediately.