Preheat oven to 350 degrees F (175 degrees C). Grease a 3-quart casserole dish.

Place milk, carrots, sweet potatoes, leeks, parsnips, celery, butternut squash, and turnip in a large saucepan; bring to a boil. Reduce heat to medium low; simmer vegetables until tender, stirring occasionally, about 15 minutes.

Stir cream cheese into vegetable mixture until melted. Stir Parmesan cheese and nutmeg into mixture. Season vegetable mixture with salt and pepper; pour into prepared casserole dish.

Stir bread crumbs and melted butter together in a small bowl; sprinkle crumb mixture over casserole.

Bake, covered, in the preheated oven until bubbly, about 30 minutes. Remove cover and cook until top is lightly browned, about 5 minutes more. Let casserole rest for 2 minutes before serving.