Pour enough water into a large pot to come about 1 inch up the side. Set a vegetable steamer in the pot, and put the squash chunks into the steamer. Cover the pot, bring the water to a boil over moderately high heat, and steam the squash for 25 to 30 minutes or until it is tender and shows no resistance when pierced with the tip of a small knife.
Puree the squash through a food mill or fine sieve set over a bowl lined with dampened cheesecloth. Wrap the cloth around the squash and, holding the ends in both hands, squeeze vigorously to remove as much of the moisture from the squash as possible. There should be about 2 cups of puree. Set it aside in a bowl.
Meanwhile, preheat the oven to 375°F With a pastry brush, spread a light coating of melted or softened butter evenly over the bottom and sides of a 2-quart soufflé dish.
In a heavy 2 to 3 quart saucepan, melt the 3 Tablespoons of butter in the oil over moderate heat. Stir in the flour and mix to a paste. Stirring constantly with a wire whisk, pour in the milk and cream, and cook over high heat until the mixture comes to a boil, thickens heavily and is smooth. Reduce the heat to low and simmer for two or three minutes. Remove the pan from the heat and stir in the squash. Then beat in the egg yolks, one at a time. Stir in the sugar, nutmeg, 1 1/2 teaspoons of salt and 1/4 teaspoon of white pepper, and taste for seasoning.
With a whisk or a rotary or electric beater—and in an unlined copper bowl, if possible—beat the 5 egg whites until they are firm enough to stand in peaks on the beater when it is lifted from the bowl. Stir two or three large spoonfuls of the whites into the squash mixture to lighten it, then gently but thoroughly fold in the remaining whites.
Pour the soufflé mixture into the buttered dish, and smooth the top with a rubber spatula. Bake in the middle of the oven for 40 minutes or until the soufflé puffs up well above the rim and the top is lightly browned. Serve at once. Serves 4 to 6.