In a small bowl, combine tuna, 1 shallot, 1 teaspoon ginger, 1/2 teaspoon lime juice, soy sauce, 1 teaspoon sesame oil and 1 1/2 tablespoons olive oil.
Using a plastic spatula gently fold the ingredients together until just incorporated.
Season, to taste, with salt and pepper.
In a separate bowl, combine salmon and the remaining shallot, ginger, lime juice, soy sauce, sesame oil, and olive oil, again using a plastic spatula to gently incorporate ingredients.
Season, to taste.
Separate the leaves of the endive.
Serve 1 1/2 teaspoons of salmon tartar in half of the leaves and fill the remaining leaves with the tuna tartar.