Butter a baking pan and spread the onions. Place over them the chicken and season to taste. Cover the chicken with aluminum foil and bake it in the oven at 170° C (338° F) for 1 hour and 15'. Uncover the pan and leave the chicken to cool off. Pour into a bowl the onions and their juices.
Bone the cooked chicken and cut it into small pieces. Then pour it into the bowl with the onions and add parsley, cheese, milk and the eggs beaten. Sauté the mushrooms for 6' in a little butter and then add the peas and carrots. Pour the sautéed vegetables in the bowl with the rest of the ingredients.
Lay the first sheet of dough in a lightly buttered round baking pan and spread over it the chicken and vegetables mixture. Straighten the surface with a spatula. Cover with the second sheet of dough, brush the pie with the remaining butter and bake it for 45' minutes at 180-200° C (356-392° F) until it turns golden brown.