Seaweed is packed with umami and seasons this halibut beautifully. If you don’t have a coffee grinder, crumble the seaweed as much as you can, to the stage that is resembles a powder.
Preheat oven to 375ºF.
Heat an oven-safe skillet over medium. Break seaweed sheet into four pieces and add to dry pan. Toast for 1 to 2 minutes or until sheet is brittle. Remove from pan and crumble into small pieces. Place in a coffee grinder and whirl until it resembles a powder.
Rub 1 tablespoon oil over halibut. Season with salt and pepper. Sprinkle fillets with seaweed powder until coated on all sides.
Heat same pan over medium-high. Add remaining oil. Place halibut in pan, skin-side up and cook for 2 to 3 minutes, or until lightly golden. Flip. Add tomatoes to pan, then mirin and let boil for 1 minute. Spoon the mirin over the fish to baste.
Transfer pan to the oven and cook for 8 more minutes, or until a knife inserted into the deepest part of the fish is hot to touch. Remove from oven and serve immediately.