Butter 10- to 12-cup casserole. Bring large pot of salted water to boil. Peel and seed squash and cut into 1-inch cubes. Peel remaining vegetables and cut into 1-inch cubes. Peel remaining vegetables and cut into 1-inch cubes. Add vegetables and bay leaves to boiling water; cook until tender, stirring occasionally, about 20 minutes. Drain vegetables. Discard bay leaves.
Puree half of vegetables in processor with half of butter and half of cream, scraping down sides of bowl occasionally. Transfer puree to bowl. Repeat with remaining vegetables, butter and cream. Transfer to same bowl. Season with nutmeg, salt and pepper. Transfer puree to prepared casserole. (Can be prepared 1 day ahead. Cover and refrigerate. Bring to room temperature before continuing.)
Preheat oven to 350°F. Bake puree until heated and beginning to brown on top, about 45 minutes. Serve hot.
