Add the flour, salt, and olive oil, then knead for about eight minutes until the dough turns smooth and elastic. Cover the bowl and let it rise in a warm spot for 45 minutes, or until doubled in size.
While the dough rises, combine the shredded chicken, ricotta, half of the mozzarella, parmesan, garlic powder, Italian seasoning, and red pepper flakes in a bowl. Season with salt and pepper, then stir everything together until evenly coated. Set the filling aside so the flavors have time to meld.
Once the dough has doubled, punch it down and divide it into two portions, one slightly larger than the other. Roll the larger piece into a circle big enough to line the bottom and sides of your pan. Roll the smaller piece into a round that will become the top crust.
Press the larger dough round into your greased pan, letting the excess hang over the edges. Spread the pizza sauce over the base, then layer in the chicken and cheese filling evenly. Sprinkle the remaining mozzarella on top before covering everything with the second dough round.
Fold the overhanging edges up and over the top crust, pinching firmly to seal in all that filling. Brush the entire top with the beaten egg wash so it bakes up shiny and golden. Cut a few small slits in the center to let steam escape while baking.
Place the pie in a 375°F oven and bake for 35 minutes, or until the crust turns a deep golden brown. Rotate the pan halfway through baking so it colors evenly on all sides. The filling should be bubbling gently at the slits when it is done.
Let the pie rest on a cooling rack for at least 10 minutes before cutting into it. This resting time allows the cheese to settle so your slices hold together. Slice into wedges and serve while it is still warm.