Preheat your oven to 400°F (200°C) and generously grease a large 9x13-inch baking dish or deep roasting pan with a little butter or oil.

Using a food processor or a manual box grater, finely grate the peeled potatoes. Working in batches, place the grated potatoes into a cheesecloth or a clean, sturdy kitchen towel and squeeze out as much liquid as physically possible into a bowl. Discard the liquid and keep the dry, starchy potato pulp.

Place the dry potato pulp into a very large mixing bowl. Gradually pour the piping hot chicken broth over the potatoes while stirring constantly with a sturdy wooden spoon. The mixture should absorb the broth and become thick and somewhat gelatinous, resembling a heavy porridge.

Stir the finely chopped onions, kosher salt, and black pepper into the hot potato mixture until everything is evenly distributed.

Spread half of the potato mixture evenly onto the bottom of your prepared baking dish. Layer the shredded cooked chicken evenly over the potato base.

Top with the remaining potato mixture, spreading it out to completely cover the chicken layer. Drizzle the melted butter evenly over the top surface to help it achieve a deeply crispy crust.

Bake uncovered in the preheated oven for 2 hours, or until the top is beautifully golden brown and very crispy. Let the pie rest for at least 15 to 20 minutes before slicing so it can set. Serve hot with butter or a dollop of cranberry sauce on the side.