Are you thinking clear or painted?
For either, I think the big concerns are going to be sealing the surface and ensuring good adhesion.
For clear - you could try to use a hardwax oil but I don't know how well it would hold up on a Vanity over time. I suspect the various cleaning agents/soaps/toothpastes/moisturizers/etc might be a bit challenging. On the other hand, I've had Osmo Top oil on the walnut island where my sink is for about 3 years now. It is holding up well but I am mindful of any standing water, and it probably could stand to be refreshed a little bit.
I also pre-treated that area w/ penetrating epoxy, which could be playing a big role in why it is doing as well as it is.
Target coatings, as mentioned above, does have some good products. I think one of them is EM9500 or something - it's a brushable product which is supposed to have very high chemical and scratch resistance.