Tokyo's Best Food Guide: Shima - The Best Grilled Steak Sandwich You'll Ever Eat! 

I've had many Wagyu Sandwiches, in most of them the Wagyu beef is deep fried.
But at Shima, you'll get a prime cut of Kobe (or Miyazaki or Kagoshima) A4 beef, grilled to perfection and placed in a pillow like bread.
That if you ask for the "Califa Special Sando"