This is the Chinese household equivalent of the better-known Japanese chawanmushi, the Japanese version being steamed in pretty little serving-sized cups with all sorts of hidden treasures. The version I grew up with, though, is plainer and is steamed in a shallow dish, usually one large enough for sharing round the dinner table. The test of a good steamed egg lies in the texture. It should be soft and delicate with a smooth surface, kind of like a savoury set custard. Done wrong, it will be rubbery with a pock-marked surface. You can make this as simple or as luxurious as you like. The simplest version is simply made with eggs and stock, or even water; seasoned simply with a drizzle of soy sauce and sizzling hot sesame oil after.
Variations:
Pork and ginger: Add fatty fried minced pork and ginger to the dish before pouring the eggs over. Season the pork and the beaten eggs with a dash of soy sauce and sesame oil first, and skip the final step.
Crab and peas: Add flakes of cooked white crabmeat and frozen peas to the dish before pouring the eggs over. Season the beaten eggs with a dash of fish sauce and sesame oil first, and skip the final step.