Keeping cabbage whole, cut out and discard core and any discolored outer leaves. Beginning at top of head and working with 1 leaf at a time, remove 6 outer leaves, rolling each one back on itself until it can be loosened intact from head and reserve. Cut remaining cabbage head into 8 wedges and cut each wedge crosswise into 3 pieces. Separate layers of cabbage pieces. Peel parsnips and diagonally cut into 1/8-inch-thick slices.
Bring a large kettle of salted water to boil and cook reserved cabbage leaves until just tender, 3 to 5 minutes. With a slotted spoon, transfer cabbage leaves to a kitchen towel to drain. Add cabbage pieces to boiling water and cook until crisp-tender, about 3 minutes. With slotted spoon transfer pieces to colander to drain and transfer to a bowl. Add potatoes to boiling water and cook just tender, about 4 minutes. With slotted spoon transfer potatoes to colander to drain and transfer to another bowl. Add parsnips to boiling water and cook until just tender, about 3 minutes. Drain parsnips in colander.
In a 12-inch heavy skillet cook onion in 3 tablespoons butter over moderately low heat, stirring, until softened. Add cabbage pieces, salt, nutmeg, and pepper to taste and cook mixture over moderate heat, stirring occasionally, until cabbage is tender, about 10 minutes. If any liquid remains in skillet, cook mixture over high heat until liquid is evaporated, about 1 minute.
If using robiola, cut into pieces. Stir robiola or mascarpone into cabbage mixture and cook over moderate heat, stirring until cheese is melted.
Preheat oven to 375 degrees F.
Butter a 2-quart ovenproof round serving dish (about 8 1/2 to 9 inches across and 2 1/2 inches deep) and line with cabbage leaves, letting leaves overhang 1 to 2 inches. Arrange half of potatoes in serving dish and season with salt and pepper. Top potatoes in dish with half of cabbage mixture and arrange half of parsnips over cabbage. Repeat layering with remaining potatoes, cabbage mixture, and parsnips, arranging last layer of parsnips decoratively around edge of casserole and leaving cabbage exposed in center. Dot parsnips with remaining 1/2 tablespoon butter. Fold cabbage leaves over parsnips and cover tightly with a double layer of foil. Casserole may be prepared up to this point 1 day ahead and chilled. Bring casserole to room temperature before proceeding. Bake casserole until heated through and bubbling, about 1 hour.
Let casserole stand 10 minutes before serving.