Any decent kitchen and bath store will have a lot of style choices and generally you would be able to get exactly the size and configuration you are looking for.

However perhaps other posters can explain how you can have drawers in a vanity that is mostly a sink since the drawers would have to deal with both the under part of the sink AND some amount of pipes below.

That is why sink cabinets (kitchen and bath) generally have doors. I have rollouts installed in my sink cabinets (kitchen and bath) so that all of the storage under the sinks is accessible.

I also wanted a drawer-heavy vanity. We got ours from Ariel Bath (which sells direct and also through lots of retailers, including Houzz). It's not perfect, but I am happy with it for the price and the customer service was great when we had some small issues. They sell at least one that is all drawers and many that are drawers except for a small set of doors in front of the plumbing with a full drawer below. IKEA also offers all-drawer vanities. (Any all-drawer options will have cutouts for plumbing built into the drawer boxes; I preferred just having the doors there and having full drawers.)

Check out the website: Bertch USA, they have lots of vanity styles and are well made. I love mine!!