What is the best way to achieve this High-Gloss White Glass Finish with wood?

What is the best way to achieve this High-Gloss White Glass Finish with wood?

The shape is probably best achieved as bent lamination or bending plywood or plywood kerfed for bending over a form.
Highly glossy surfaces can be achieved with wood -- consider a piano's finish -- with a lot of work carefully applying the finish, buffing it to smoothness, and repeating . But I'm guessing that in the case you're showing us, that's probably plastic ("melamine" or similar) as the outer surface of the laminated skin of the desk, unless this is a very high-end piece.
The main use I see here for a router is trimming the edges of the skin, and maybe in the drawer joinery (though I wouldn't be surprised to find them built with dowelled joinery). Maybe some template routing when building the bending forms or support framework under the skin, to make sure shapes match.