Fill a deep pot with water ⅔ of the way, and place the chicken inside. Season with 1 tablespoon salt, cover and bring to boil on high. Lower temperature to medium and cook for 45 minutes or so.
Remove off heat.
Take the chicken out, but keep the broth. Take the skin off the chicken, separate meat from the bone and shred it.
In a large mixing bowl, combine shredded chicken, onion, 1 tablespoon salt and and pepper. Mix well. Heat oven to 400°F (200°C).
(If using tortillas instead of hard phyllo, bake them for 5-7 minutes on medium rack, until they are tough. Take the tortillas out but keep the oven on.)
Oil a baking pan (one used was approximately 11x16 inches or 40x27cm). Make one layer from hard phyllo or hard tortillas (you may have to break it in parts to make it fit). Use a ladle to pour a couple of scoops of chicken broth onto the layer. Spread a few handfuls of shredded chicken filling over it. Cover with another layer of phyllo/ hard tortillas, and repeat.
Repeat until you're out of ingredients, making sure the pie has phyllo/ tortillas on top. Pour a few more scoops of broth on top and place in the oven.
Bake 20 minutes on 400°F (200°C), then lower to 360°F (180°C) and bake another 15 to 18 minutes. During baking, moisten the pie with a few more scoops of the broth once or twice.
Take out and cover with a kitchen towel. Let cool off for 15 to 20 minutes.