Combine the lime juice, jalapeño, brown sugar, fish sauce, garlic, and ginger in a small bowl. Whisk in both oils in a slow stream; set aside.

Prepare a medium-high (400°F to 475°F) gas or charcoal grill fire.

Pat the steak dry and season well with salt and pepper. Oil the grill grate and grill the steaks, turning once, until medium rare (135°F), about 6 minutes total. Transfer to a cutting board, let rest for 5 minutes, and then thinly slice across the grain.

Meanwhile, in a large bowl, combine the mango, onion, lettuce, and 2 Tbs. of the cilantro. Toss with enough dressing to coat, divide the salad among 4 plates, and top with the steak. Drizzle the remaining dressing over the steak, sprinkle with the remaining cilantro, and serve.