I am confused. Your post sounds like you want to replace your current countertop with a new countertop. However, that would be simple. Am I incorrect about what you want to do? Do you really want to replace your entire vanity with a new vanity/countertop combo?

To replace a countertop on an existing vanity (or to purchase a countertop for a new vanity that doesn't come with a countertop) - you simply have one fabricated. A fabricator will template the area for the new countertop (to make sure that it fits exactly along the back wall and the wall where the vanity will be flush. Walls are rarely ever plumb + square = having a template made will make the countertop fit the space exactly as needed.

A fabricator will have access to slabs + possibly prefabricated countertops (less expensive) + remnants (the least expensive option).

I don't know where you live - my city happens to be a regional area where basically every countertop manufacturer has a warehouse = lots of options.

If you are tyring to find a vanity + countertop combo - I don't think that you will find one with one side flush with the cabinet and the other side with a 1" over hang.

Same comments as the above from @dani_m08

Thank you