Heat the oven. Arrange a rack in the middle of the oven and heat to 375°F.
Shred the onions and potatoes with a food processor. Using the shredding disk of the food processor, shred the onions and potatoes. You will likely have to do this in 4 batches, simply transfer each batch of shredded onion and potato to a large bowl while you continue shredding.
Make a cheesecloth tourniquet and squeeze the liquid from onions and potatoes. Lay 1/4 of the grated onion and potato on a large triple layer of cheesecloth or clean, lint-free kitchen towel. Gather the corners and tie around the handle of a wooden spoon. Dangle the bundle over a medium bowl, then twist and squeeze the onion and potatoes as hard as you can until no more liquid comes out. Do not discard the liquid. Transfer the onion and potatoes to a clean, large bowl. Repeat this squeezing process with the rest of the grated onion and potato, replacing the cheesecloth if it tears.
Pour off the liquid, but leave the potato starch. Give the liquid a few minutes to allow the potato starch to settle, and then pour off and discard the liquid but leave the potato starch; set aside.
Beat the eggs. Place the eggs and egg whites in the bowl of a stand mixer fitted with the whisk attachment. (Alternatively, use an electric hand mixer and large bowl.) Beat on medium-high speed until lightened in color and doubled in volume, 3 to 4 minutes.
Add the schmaltz, potato starch, baking powder, salt and pepper, then toss with onions and potatoes. Add the reserved potato starch, 1/4 cup of the schmaltz or oil, baking powder, salt, and pepper. Beat on medium speed until combined. Add the reserved onion and potato and use your fingers to toss them with the egg mixture until evenly coated.
Grease and preheat the baking dish. Brush a 9x13-inch baking dish with the remaining 2 tablespoons of schmaltz or oil. Heat in the oven for 5 minutes.
Bake the kugel. Carefully transfer the mixture to the preheated baking dish and spread into an even layer but do not press down on it. Bake until golden-brown and an instant read thermometer registers at least 160°F, 40 to 50 minutes.
Broil the kugel. Turn the broiler to high. Broil the kugel until the top is richly browned, 2 to 3 minutes. Cut into generous slices and serve immediately with a sprinkle of parsley or chives.
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