How to Make It
Make the sauce In a food processor, pulse the mushrooms in 4 batches until finely chopped; transfer to a 12-quart pot. Add the leeks, carrot, garlic, bay leaves, salt, thyme, peppercorns and curry powder to the food processor and pulse until very finely chopped; transfer to the pot. Add the cream and 1 quart of water and bring to a boil over high heat, then simmer over moderate heat, stirring occasionally, for 1 hour.
Strain the stock through a fine sieve set over a large heatproof bowl, pressing on the solids; discard the solids. Return the stock to the pot and boil over moderately high heat until reduced to 3 cups, about 10 minutes. Pour the stock into the bowl.
Wipe out the pot and melt the butter in it. Whisk in the flour and cook over moderate heat, whisking often, until well browned, about 7 minutes. Gradually whisk in the stock until smooth and bring to a boil. Simmer over moderately low heat, whisking often, until thickened and no floury taste remains, about 15 minutes. Scrape the sauce into the bowl.
Make the filling Wipe out the pot and melt the butter in it. Add the shallot and garlic and cook over moderately high heat, stirring, until softened, about 2 minutes. Add the rutabaga, turnips, sunchokes, carrot, parsnip and a generous pinch of salt. Cook, stirring occasionally, until just softened, about 7 minutes. Add all of the mushrooms and cook, stirring occasionally, until tender and their liquid evaporates, 10 to 12 minutes. Add the sauce and cook over moderately low heat, stirring often, until the vegetables are coated in a creamy sauce, 10 to 15 minutes. Remove the pot from the heat and stir in the herbs. Season with salt and pepper. Spread the filling in a 9-by-13-inch gratin dish.
Make the topping In a large saucepan, cover the potatoes, chestnuts and parsnip with the cream and 1 quart of water and bring to a boil over moderately high heat. Stir in the nutmeg and 1 tablespoon of salt and simmer over moderate heat, stirring occasionally, until the vegetables are tender, about 30 minutes.
Drain the vegetables in a colander set over a heatproof bowl. Transfer half of the vegetables to a food processor, add ¾ cup of the cooking liquid and puree until smooth. Scrape into a large bowl. Repeat with the remaining vegetables and another 3/4 cup of the cooking liquid. Let the puree cool slightly, then stir in the egg yolks and chopped herbs and season with salt. Spread the topping over the filling and swirl decoratively.
Preheat the oven to 375°. Bake the pie for about 40 minutes, until the filling bubbles. Turn on the broiler and broil 8 to 10 inches from the heat for 2 to 3 minutes, until the top is lightly browned. Let stand for 20 minutes. Sprinkle with salt and serve.