There are two dishes called alabaster: one is English and one is American. Both are very simple dishes.
The American version of alabaster is a simple, savoury Shaker dish made from boiled and mashed potatoes, turnip, and cream. The two root vegetables are cooked separately, to avoid the turnip flavour overwhelming the potato, they are mashed separately as well, and seasoned simply with salt and pepper. The turnip is then stirred into the mashed potato, but not completely, so that swirls are still visible. It was named after the silvery-white swirled colour of the dish.
The English alabaster dish is a sweet. It’s a pudding, made from warmed cream, that has gelatin and some sugar stirred into it, and is let set in a mould until it is firm. It is then turned out of the jelly mould and decorated with fruit.