Rub bottom of 8 1/2" x 12" baking pan with olive oil. Shingle half the rutabaga slices to cover bottom of pan, overlapping slices no more than 1/2". Sprinkle lightly with salt and pepper.
Shingle 1/5 of potato slices over rutabaga; season lightly with salt and pepper. Pat or mist lightly with oil. Spread half the onions evenly over potatoes. Layer half the parsnip slices over onions; follow with another layer of potato slices. Pat or mist lightly with oil; season lightly with salt and pepper.
Spread potatoes with 4 oz. duck prosciutto; sprinkle with 2 oz. Pecorino Romano. Repeat layering and seasoning with rutabaga, potato, onion, parsnips, potato, duck, cheese, and final layer of potato.
Pat or mist lightly with oil; season with salt and pepper. Cover pan tightly with foil.
Bake 45 - 50 minutes. Remove cover; pat or mist lightly with oil; sprinkle with herbs.
Bake, uncovered, until top layer is lightly brown, 15 - 20 minutes. Allow to set 10 - 15 minutes. Slice and serve.