While I think the wood idea is a lovely compliment to the brown-gold veins in the granite,what concerns me is that if the only darker tones are in the granite and the vanity, it may stand out as not belonging in the space. I think I would be inclined to go with a painted vanity, but in more of a vanilla or something a bit warmer than white, to work with your tile. I would not do the walls the same color as the granite, but instead a darker shade of the color, for interest. What color will your faucets, lights and doorknobs, etc. be? You could also enrich the space by choosing a deep color for your towels.

I did as Kats suggests several years ago with former house. I had room for a spacious vanity with a remodel and opted for one right sink, a bank of wide drawers for storage, and a much needed built in laundry hamper. A local cabinet maker made the vanity and a towel tower, GC installed corian top. I chose alder with a whitewashed and glazed finish, it was not a budget breaker.

This kind of monolithic wall-hung vanity tops are probably custom. If you don't mind white, look at MTI counter-sinks. If you simply want wall hung and would like drawers, look at wall hung vanities like these at DecorPlanet. I am not saying that these are good quality or not, just wanting you to see them for their style. You can have a wall-hung, minimalist vanity with drawers in it. You can search for wall-hung and modern vanities with the size you need at build.com, Qualitybath.com, and Wayfair, too. Duravit and Nameeks are two European companies that also do wall-hung vanities and counter-sinks.

Glaze has no place to hang up on a slab door. Most manufacturers won’t do slab or shaker doors with glazing for that reason. Glaze is supposed to hang up in the details, and you need a door with some of those details to make it show. A floating vanity that’s mounted at only 6” off the floor is doable, but it’s more difficult to clean under than one mounted the more traditional 15” off the floor. The traditional height of floating vanities is 18”H and 21” H. Have you lived with a vessel sink before? They are gorgeous! But they have more water on the counter and more water running off of the counter than an undermount sink. They’re more work to clean and maintain than an undermount. I just want to make sure you have considered all of that extra work before the decision finalization. :-)