North American white and red oak have open grain. It's especially present when the boards are flat cut. When you stain the wood to get a medium color like your door, the grain turn black from the stain. Rift and quarter-sawn cut the boards at an angle that minimizes the open grain and the black grain pattern. To deal with that you can fill the grain with a light color paint or any color lighter than black. Cerise is a technique. Also pickling. Then you can add a topcoat of clear finish. The door you show looks like it got a light grain fill and a satin topcoat. It looks good in the full picture. As an aside, European and French Oak are different oak species with more dense less open grain. You can see that on IKEA Vedhamn doors. VEDHAMN oak fronts - IKEA

IKEA uses European Oak. They are about the only place where you can get European Oak cabinet doors and drawer fronts in the US. . . .and you'll save a lot of money.

DOCA cabinets in Spain also makes cabinets. DOCA: Kitchen furniture and wardrobes of the highest quality (docakitchens.com) i think they have a rep on Long Island.