Steam carrots until tender in a medium saucepan over simmering water, about 20 minutes. Purée in a food processor.
Preheat oven to 200°C. Coat an 8-cup soufflé dish with non-stick cooking spray.
Heat the oil in a small saucepan over medium heat. Add onion. Sauté until softened, about 5 minutes. Stir in the flour and cook, stirring occasionally, for 1 minute.
Stir in the milk and bring the mixture to the boil, stirring constantly. Simmer for 2–3 minutes or until slightly thickened. Lightly beat the egg yolks in a large bowl. Gradually pour in the milk mixture, whisking constantly. Stir in the carrot puree and the grated zucchini. Stir in the salt, pepper and nutmeg.
Beat the egg whites in a medium bowl until soft peaks form. Fold whites, a third at a time, into vegetable mixture. Spoon into the prepared dish. Bake until puffed and golden, 30 to 40 minutes. Serve at once.
The slightest amount of fat from butter, oil or egg yolk will prevent egg whites from forming soft peaks when whipped. To avoid this, make sure the bowl is clean and the egg whites are carefully separated, with not a speck of yolk.