I use jlcpcb, they're common in the prototype and hobby domains. But there's quite a few board houses in taiwan and china that do this, definitely shop around.
The annoying part is getting the bom and component placement files correct. I use kicad since it's free, and there's solid instructions from most houses on what they need.
JLBPCB does small runs cheap as a loss leader, so they get the production runs, if any, later. Also, they get to see what people are doing, in case something interesting goes by.
There's also a suspicion that JLBPCB may be encouraged to do this by the Party, to discourage other countries from maintaining an independent prototyping capability.
Ah, really interesting points, thanks. It definitely seems too cheap to be true.