In a large pot, bring the water to a boil, then add the ground almonds. Bring back to a boil over low heat, then turn off the heat, cover and leave 15 minutes to infuse. Filter through a fine sieve.

In a large bowl, beat the egg yolks with the sour cream. Add the warm infusion a little at a time, stirring all the while. Allow the mixture to cool. Season with salt and pepper to taste.

Cut the melon in half and remove the seeds. Cut the flesh into small dice, and add to the soup. Serve with a garnish of dill and almond slivers.