To make the dressing, mix together the lime juice, fish sauce, cilantro, mint, chiles, lemongrass, ginger, and brown sugar.
Preheat the broiler. Season the steak with salt and pepper. Broil for 3–4 minutes on each side, until medium-rare. Transfer to a carving board and let cool. Carve into thin slices.
Soak the noodles in a bowl of very hot water about 10 minutes, until softened. Drain well and rinse under cold running water. Cut into manageable lengths with kitchen scissors.
Heap the noodles, papaya, and steak in a platter. Add the dressing and peanuts and toss. Serve immediately.