*Note: Suggested cheeses are either Mizithra or Kefalotyri. If unavailable, Parmesan or Romano could be substituted. :-( Remove the bones and skin from chicken and discard. With your fingers tear the chicken into strips, not too small. Set aside while you prepare the sauce. Melt the 4 T butter in a heavy pan, then blend in the flour, without scorching, over medium heat. Remove from the heat for a minute and stir in the warm broth, then return to the heat and cook gently until the sauce boils. Cool. Mix in the milk if the sauce seems too thick, then add the eggs, cheese, a little salt, pepper, nutmeg, and thyme. Butter a 9 x 12 x 3-inch baking pan and in it spread 6 filo sheets, brushing each with melted butter. Pour in the chicken filling, then cover with the remaining filo sheets. Tuck the top filo over the bottom and flute the edges. Score the top 3 filo sheets with a sharp knife. Bake in a moderate oven (350 F) for 40 minutes, or until crisp and golden chestnut in color. Remove from oven and let stand for 15 minutes before cutting into 9 to 12 squares. Serve warm. (Serves 9 to 12) Note: In Epirus, Kotopita is sometimes made with a large amount of onions. If you would like to try it, use the recipe above plus 1 pound of Spanishtype onions. Peel and slice the onions, boil in water for 5 minutes, and drain. Prepare the sauce without the cheese and bake the chicken and onions in the sauce, between homemade filo, preferably, or commercial filo.