Clean the mussels at the beginning in sufficiently cold water, remove the beards and rinse them again under cold running water.
Discard all damaged mussels and all mussels that are not closed.
Peel and dice the onions, rinse and roughly chop the parsley, then sauté the onions and parsley in a large diameter saucepan in a small amount of oil and butter, extinguish with white wine, season with salt and pepper and simmer on low heat for about 5 minutes. Then put all the mussels in the saucepan and cook on high, covered and at maximum temperature. When the mussels are done, turn down the heat and cook the mussels for about 5 minutes until they are all open. Remove the mussels from the broth, discard closed mussels, cool mussels, then scoop out and set aside.
For the soup, rinse the squash, remove the stem base, then quarter the squash lengthwise and remove the seeds along with their fibrous surroundings, finally cut the squash into even pieces. Remove the peel from the onion and chop it coarsely, peel the potatoes and cut them into cubes, rinse the leek and also cut it into pieces with the leek greens, sauté the whole thing together in a little bit of butter and oil, then add the finely chopped garlic, season with salt, season with pepper. Strain the mussel broth, add a little bit of it to the cooked mussels.