1. Place parsnips in a large saucepan; add enough water to cover. Generously salt water and bring to a boil over high heat. Reduce heat to a simmer; simmer until tender, 10 to 15 minutes. Drain.

2. Preheat oven to 350 degrees. Puree parsnips in a food processor or food mill. If using a processor, take care not to overprocess or they will become gluey.

3. Transfer pureed parsnips to a large bowl; whisk in salt, sugar, melted butter, heavy cream, and Madeira.

4. Spoon parsnip mixture into a 1-quart baking dish. Dot top with butter and sprinkle with breadcrumbs or chopped nuts. Bake 20 to 30 minutes. Serve.