How to Make It
Preheat the oven to 450°. In a medium saucepan, heat the vegetable oil until shimmering. Add the shallots and cook over high heat, stirring occasionally, until golden and crisp, about 6 minutes. Using a slotted spoon, transfer the shallots to a plate. Reserve the shallot oil.
Working in batches, squeeze out as much of the liquid as possible from the potatoes and transfer them to a large bowl as you go. Add the grated onion, potato starch, salt, black pepper and grated nutmeg and stir well. Stir in the whole eggs, egg yolks, olive oil and boiling water, then stir in the fried shallots.
Heat two 8-by-11 1/2-inch flameproof or enameled cast-iron baking dishes over high heat until they are very hot to the touch. Add 2 tablespoons of the shallot oil to each baking dish and heat until smoking. Carefully spread the potato mixture in the sizzling baking dishes.
Transfer the potato kugels to the oven and bake them for 20 minutes. Lower the temperature to 375° and bake the kugels for 40 minutes longer, until golden and crisp on the sides.
Preheat the broiler. Broil the potato kugels as close to the heat as possible for about 2 minutes, until they are browned and crisp on top. Let the potato kugels stand for 20 minutes before cutting into squares and serving.