For the chicken soup, place all the soup ingredients into a large saucepan, cover with cold water and bring to the boil. Reduce the heat and simmer for 1 hour.
Remove the chicken and set aside to cool slightly. Remove the meat from the chicken and slice into chunks.
Strain the liquid through a muslin cloth into a clean saucepan. Let the liquid drip through rather than trying to push it through to create a clear broth.
Meanwhile, for the dumplings, beat the eggs, oil, half of the stock and matzo meal in a bowl to form a thick paste. Whisk in the remaining stock and dill and season, to taste, with salt and freshly ground black pepper. Set aside for one hour.
Using oiled hands, roll the dumpling mixture into small balls, approximately 2.5cm/1in in diameter. Meanwhile, heat the chicken stock until simmering and cook the dumplings for 30 minutes.
To serve, reheat the chicken broth, if necessary, and place some cooked chicken into the bottom of each of 6 serving bowls, pour the chicken broth on top and add a few dumplings.