Preheat the oven to 400 degrees F.
Combine the potatoes and leeks on a sheet pan in a single layer. Add the olive oil, 1 teaspoon salt, and 1/2 teaspoon pepper and toss to coat the vegetables evenly. Roast for 40 to 45 minutes, turning them with a spatula a few times during cooking, until very tender. Add the arugula and toss to combine. Roast for 4 to 5 more minutes, until the arugula is wilted. Remove the pan from the oven and place over 2 burners. Stir in the wine and 1 cup of the chicken stock and cook over low heat, scraping up any crispy roasted bits sticking to the pan.
In batches, transfer the roasted vegetables to a food processor fitted with the steel blade, adding the pan liquid and about 5 cups of the chicken stock to make a puree. Pour the puree into a large pot or Dutch oven. Continue to puree the vegetables in batches until they're all done and combined in the large pot. Add enough of the remaining 1 to 2 cups of stock to make a thick soup. Add the cream, creme fraiche, 2 teaspoons salt, and 1 teaspoon pepper and check the seasonings.
When ready to serve, reheat the soup gently and whisk in 2 tablespoons white wine and 1/4 cup of Parmesan. Serve hot with an extra grating of Parmesan and crispy shallots, if using.
Heat the oil and butter in a saucepan over medium-low heat until it reaches 220 degrees F on a candy thermometer.
Reduce the heat to low, add the shallots, and cook for 30 to 40 minutes, until they are a rich golden brown. The temperature should stay below 260 degrees F. Stir the shallots occasionally to make sure they brown evenly. Remove them from the oil with a slotted spoon, drain well, and spread out to cool on paper towels. Once they have dried and crisped, they can be stored at room temperature, covered, for several days.
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