Filling:

In a medium pot, over medium heat, add the chicken and the olive oil. Stir in the garlic, onion, dill, celery, carrots, salt and pepper. Add the chicken stock and bring to a boil. Turn the heat down and let it simmer for 15 minutes.

Sauce:

In another medium pot bring the milk to a boil over low heat. At the same time, melt the butter in another pan. Add the flour to the butter and mix well on low heat until the flour absorbs all of the butter. Be sure not to burn the butter! When the milk reaches the boiling point, slowly whisk it into the flour mixture until it thickens, removing any lumps. Whisk in the Parmesan and the egg. Remove the sauce from the burner and let it cool for 10 minutes. Set aside and go back to the filling.

The chicken mixture should be fully cooked by now. Strain the mixture to remove any liquid. Let it sit for 15 minutes. Mix the sauce into the chicken mixture. Add the Parmesan and feta cheese and mix well.

Preheat oven to 350 degrees F.

Butter an 8 by 8-inch baking dish. Layer 7 sheets of phyllo dough in the bottom of the dish making sure to lightly brush each 2 sheets with melted butter. Make sure to press the sheets against all sides of the baking dish. Fold the sheets in half, and evenly spread them with the filling. Put another 7 sheets of phyllo, prepared the same way on top of the filling, pressing the dough around the edges of the dish. Lightly brush melted butter on the top layer. Cut through the dough to make 4 squares. Make sure you cut through the bottom layer. Sprinkle a little water on top to keep it from drying out. Put the dish in the oven and bake it until golden brown, about 40 to 45 minutes. Remove the dish from the oven and let it cool for 20 minutes before serving. Most commonly served with salad, but it's a great dish with vegetables or by itself.