Combine remaining 1/4 teaspoon salt, milk, 1/2 cup cheese, pepper, nutmeg, eggs and egg whites in a large bowl, stirring with a whisk. Stir in squash and onion mixture. Add bread, and stir gently to combine. Let stand 10 minutes. Spoon into a 2-quart baking dish coated with cooking spray. Sprinkle with remaining 1/2 cup cheese. Bake at 180°C for 45 minutes, or until pudding is set and lightly browned.