Heat oil in a frypan over medium heat. Brown the mince with the shallot, 1/2 teaspoon salt and pepper. Let cool, then add the dill and egg and mix well. Refrigerate.
Knead together the flour, 1/2 teaspoon salt and 2 beaten eggs. If the dough is too dry, gradually add the remaining egg. The dough should be soft but not sticky. Transfer to a floured surface and knead 10 minutes until elastic.
Roll out the dough and cut into 6cm diameter circles. Place a tablespoon of filling on each circle, then fold up the dumplings and seal with a little water.
Bring the chicken stock to a simmer in a large saucepan. Add the dumplings and simmer 12-15 minutes. Serve.