In a shallow, nonreactive dish just large enough to hold the flank steak comfortably, combine the steak with 3 tablespoons of the lime juice, 2 tablespoons of the oil and 1 tablespoon of the fish sauce.
In a food processor, combine the remaining 1/3 cup oil, half the cilantro, the remaining 3 tablespoons lime juice, the remaining 2 tablespoons fish sauce, the ginger, garlic, jalapeño and soy sauce. Process until smooth. Add 2 tablespoons of the pureed mixture to the marinating steak. Over and let stand at room temperature for 2 hours, or in the refrigerator overnight. Return the steak to room temperature if chilled.
Heat a large, heavy skillet over medium-high heat until hot. Lift the steak from the marinade, reserving the marinade, and pat the steak dry. Lay the steak in the skillet and cook until well-browned, about 6 minutes. Turn and cook until well-browned on the other side, another 5 to 6 minutes for a rare steak, or until done to your liking. Turn the heat to low and add the marinade to the pan, turning the steak in the marinade to coat.
Take off the heat and transfer the steak to a cutting board. Let rest for 5 minutes and then cut the steak across the grain at an angle into thin slices.
In a large bowl, toss the lettuces with the remaining ½ cup cilantro, mint, basil and onion with about half of the dressing. Divide among 6 plates. Arrange the tomato wedges and cucumber slices around the dressed greens on the plates. Arrange the sliced steak over the greens. Serve, passing the remaining dressing at the table.