The Greek version of Chicken Pot Pie that uses phyllo dough as a crust. It can be made in any deep casserole or pie pan.
Place the chicken meat in a large pot and pour the chicken broth over the meat. (the broth can be made with bouillon.) Simmer for 15 minutes, if boneless or 30 minutes if the chicken has bones and skin. Pull the chicken out of the broth with tongs and let cool. Retain the broth for the sauce.
Preheat your galley oven to 350º. While the chicken cools, make the white sauce. Chop the scallions until you get one cup. In a large pot melt 1/4 cup butter and sauté the scallions for about 3 minutes. Add the flour and cook for another minute. Add 3 of the 4 cups of chicken broth to the pan and cook over low heat until thickened. If it seems too thick, add some more broth. Turn off the burner and set aside to cool down a bit.
Skin and debone the cooled chicken meat, if you used bone-in chicken. Shred the chicken meat into bite size pieces.
Add the chicken meat to the sauce. Mince the parsley, dill and mint. Add to the chicken sauce, blending in well.
Lightly beat the 3 eggs. Combine the feta cheese and eggs into the sauce. Stir in well. Add a teaspoon of pepper and salt to taste. Set aside while you prepare the phyllo dough.
Melt the remaining 3/4 cup of butter in a small sauce pan. Brush a deep dish pie pan with butter. Lay one sheet of phyllo dough in the pan and brush with more melted butter. Butter as far to the edges as you can. Repeat with 6-7 more phyllo sheets, buttering each one. Be sure to not get the phyllo dough wet.
Gently pour the chicken mixture into the prepared pie pan.
Layer another sheet of filo dough on top. Brush with butter. Repeat with the remaining filo sheets, brushing each with butter. Tuck the edges into the pie pan and butter the edges well.
Place in your preheated oven and let bake for 45 minutes. Check it after 30 minutes. If it seems to be browning too quickly, place a sheet of foil on top.
Let rest for 10 minutes before serving.