In a large stockpot, combine the chicken pieces, chopped onions, salt, pepper, and dried savory with the water; bring to a boil and simmer for 45 minutes until the chicken is tender.

Remove the chicken from the pot, shred the meat into bite-sized pieces discarding bones and skin, and keep the broth boiling on the stove (you will need about 12-14 cups of broth).

While the chicken cooks, grate the peeled potatoes into a large bowl of cold water to prevent discoloration.

Working in batches, transfer the grated potatoes to a cheesecloth or fine mesh bag and squeeze vigorously to remove as much liquid as possible, discarding the starch water.

Place the dried potato pulp into a large heat-proof mixing bowl and measure the quantity of boiling broth to match the amount of liquid you squeezed out (roughly 12 cups).

Gradually whisk the boiling chicken broth into the potato pulp a few cups at a time until the mixture transforms into a thick, gelatinous consistency similar to porridge.

Preheat your oven to 375°F (190°C) and generously grease a large 13x18 inch baking sheet or roasting pan with butter.

Spread half of the scalded potato mixture evenly across the bottom of the prepared pan.

Distribute the shredded chicken and cooked onions evenly over the bottom potato layer.

Cover the meat layer with the remaining potato mixture, using a spatula to smooth the top surface evenly.

Dot the surface generously with the small cubes of salted butter to ensure a deep golden, crispy crust.

Bake in the preheated oven for 2 hours, or until the top is well-browned and crispy.

Remove from the oven and let the pie stand for 15 minutes to set before cutting into squares and serving warm.