1. To prepare the tuna, place the scallions over a low flame, an electric burner or charcoal. Cook until they are slightly charred all over, turning as necessary. Remove them from the heat and place them in a large bowl.
2. Add the red wine, red wine vinegar, soy sauce, sesame oil, paprika, sliced ginger and garlic.
3. Cut the tuna lengthwise into 4 portions of equal size and weight. Add the slices to the marinade and let stand for 2 hours.
4. To prepare the sauce, combine the shredded ginger, white wine, rice vinegar and shallots. Cook for 10-15 minutes, until the liquid is reduced to about 3 tablespoons. Add the cream and cook down about 5 minutes. Gradually add the butter, beating vigorously and constantly with a wire whisk. Add salt and pepper.
5. When ready to cook the tuna, preheat a charcoal, gas or electric grill. When it is very hot, brush lightly with oil. Add the tuna strips and cook 1 1/2 to 2 minutes on one side. Turn and cook 1 1/2 to 2 minutes on the other side, or to the desired degree of doneness.
6. Slice the tuna on the diagonal into 1/4 inch thick slices. Arrange the slices, slightly overlapping and in a fan shape on a plate. Spoon the sauce over the base of the "fan". 4 servings.
