You find a local source for cabinetry, and you find one that has a white oak finish you love. This is best achieved in a FACTORY finish.

Before all that? You consider your kitchen layout and its function. The appliances. Appliances are the driver of any kitchen. then you consider the storage requirements for your lifestyle. Cooking, entertaining. You move on to style/ finishes in cabinetry and flooring. They are NOT independent of one another......and simultaneously consider the flooring in the remainder of your home if this is reno ........or new build. The

Then you consider counter tops, LIGHTING, the style and flavor you want to achieve.......and you will notice I have not used the word "backsplash" yet. Ideally, it is selected last. : )

All of this of course, in combination with your budget.

The single best route through all the aforementioned? An independent kitchen designer. On your site. In YOUR kitchen

Your kitchen is not an online, just get THIS project. Unless you favor major disappointment.

I am sorry to say that white oak is extremely expensive even with just a clear finish. With a specialized finish, its expense is way up there. Since you mentioned that the cost is a concern, I think white oak that looks like your OP photo is out of your reach (and most people's). If that coloration is what you like, perhaps you would like maple cabinets in the Danish Modern style. I am not saying they will look like white oak. But they have the light color you like, and are more affordable.

If you want oak to not look like oak, then pick another wood. I'm not even certain that cabinet is oak.

Who said that was oak at all ,pretty grainless for oak. I do agree better to go a different wood if you like that bleached sort of look. This is the definition of fumed wood not what you see there at all IMO

Ammonia fuming is a wood finishing process that darkens wood and brings out the grain pattern. It consists of exposing the wood to fumes from a strong aqueous solution of ammonium hydroxide which reacts with the tannins in the wood. The process works best on white oak because of the high tannin content of this wood. Wikipedia

North American white oak when flat cut has an open grain that finishes dark. If this is oak, it could be European or French oak. A European cabinet company like Doca could be a source.

Thank you for all the comments. The reason I am certain that it is white oak because the article where I found the picture specified that. It could be European oak. I do not know how they create that finish that you cannot see the grains. . Doca cabinets do look similar. It will all come down to balancing cost- shipping to the US is expensive too. I am considering maple- as Miranda suggested. Jan, I saw your post about your kitchen, it is beautiful- hopefully I find someone local who could work out the stain or dye for me.

https://ruemag.com/home-tour-2/from-remodel-to-rebuild-an-oklahoma-home-with-west-coast-vibes-by-hanieh-pace-of-ivy-house-interiors

The designer says it's white oak but doesn't identify the millwork shop.