Yes in USA you can get pretty reasonable custard tarts as a Chinese desert, often available in Dim-Sum restaurants. The ones I’ve tried aren’t as heavy or sweet as the English versions though.
Brown sauce is IMHO at its very best when had with a full English Breakfast.
The easiest way to get British-style custard is to use Bird’s Custard Powder.
That’s what I think of too, when I hear “brown sauce.” At your average Chinese places, it seems absolutely every stir-fried dish comes in the exact same brown sauce, giving every dish the exact same taste, no matter what the advertised main ingredient is.
I’m surprised too, but that my vague impression wasn’t 100% off base. I’d always had the idea that it involved meat juices/gravy, and some sort of alcohol. No alcohol(rum, likely), but there is meat juices involved. hmm.
Good gravy!
Oh dear.