Ya know, I never even thought about places making it differently. Chineese restaurants here make a flavorful chicken stock w/bits of green onion, an occational bit of mushroom and the added eggs. It's a thin, watery textured soup, no cornstarch. I guess you just need to ask..
Maybe with that recipe that Leenie postd, you could substitue 2 more egg yolks in place of the cornstarch to thicken it a bit. It sounds good! I might give that a shot for lunch! Thanks Leenie...