Conestoga might have something

Here is a link that might be useful: Conestoga

Do you have a photo? Depending on the grill it might be possible to replace just that, unless of course you would prefer a solid door.

Here's a company that makes custom grilles, for example. It's not cheap, but you wouldn't need much for a vanity. Someone in the kitchens forum used them for kitchen cabinets and was pleased with the quality.

Here is a link that might be useful: Brass grilles shop

Barkers has a cabinet forum, you might ask there? They do sometimes take a little long to reply.

Here is a link that might be useful: barkers forum

If I'm understanding what I'm looking at, the very first edge profile on the Conestoga page is the right one. That lip closes against the face frame.

I'd prefer solid doors over replacing the metal mesh. I've never liked it, and it's one of the first things the Realtor grimaced at. If I can't find them to buy, my husband is a woodworker and could crank them out fairly quickly. He doesn't really have time, though, so I'd rather be able to order them.

Thanks for the sources.