Audrey C: "I'm trying to do something similar with a bathroom vanity having no counter, just a sink..."
You could use one of these Fresca Drop-in Sinks. They're designed to fit Fresca vanities but you can buy them separately. You would have to build a cabinet with exactly the same length and width as the corresponding Fresca model to be sure the sink would fit. It may be easier to just buy a Fresca vanity if you could find one that met your appearance requirements.
American Standard and Swiss Madison also make such sinks and I'm sure there are many others (check build.com).
Q