Coarsely chop the walnuts and almonds. Drain the mozzarella and squeeze it lightly between kitchen paper. Wash the herbs, shake dry, put 8 basil leaves aside for garnishing. Cut remaining herbs into fine strips.
For the vinaigrette, mix vinegar, salt, pepper and sugar. Fold in olive oil.
From the middle of the melon, cut 4 slices about 2 cm thick. Cut off the skin all around the melon, remove seeds if necessary. Put 1 melon slice on each plate. Pluck the mozzarella and spread on top. Add the herbs. Sprinkle evenly with the vinaigrette. Sprinkle with nuts. Garnish with basil leaves. Serve with muck sticks* or baguette.
*The so-called Muckstangen are a combination of grissini and baguette.