In a small saucepan, combine the ginger, pineapple juice, vinegar, soy and brown sugar, and bring to a boil over high heat. Reduce heat to low. And simmer until volume is reduced by half, about 20 minutes. Add the ketchup and cook 5 minutes more. Remove from heat, stir in the lime juice cilantro and white or black pepper and set aside.
Sprinkle the tuna generously with salt and pepper, then grill over a medium are for about 3 minutes a side, or until a peek in the interior shows some pink. (This is for medium rare; if you like it better done, keep cooking until it reaches the stage you like.) During the last minute of cooking, paint each steak with a couple of tablespoons of the glaze.
Remove tuna steaks from the grill, top each with a tablespoon or two of glaze, and serve at once. Pass remaining glaze separately.
1 tablespoon minced ginger
1 cup pineapple juice
1/2 cup white vinegar
1/4 cup soy sauce
1/4 cup brown sugar
1/2 cup tomato ketchup
1/4 cup lime juice
1/4 cup finely chopped cilantro
1 tablespoon freshly ground pepper
2 pounds tuna steaks, cut into portions or four 8-oz steaks 1.5inches thick
salt and freshly cracked black pepper