Photo?

You can either repurpose a dresser or some sort of furniture like that or buy any vanity without the traditional top and have one made by a company that fabricates them in your area. It does almost sound (from your description) like a drop in though and not a vessel. Can you post a pic?

I think you're talking about semi-recessed sinks. What size vanity do you need? We have vanities without a top, so you can pick your sink and counter top of choice, as opposed to vanities that already come with the countertop and sink.

That is something you talk to your countertop fabricator about. After you make sure that thhe vanity that you've chosen is short enough to accomodate the sink without making you feel like you're sitting at the kids table.