To make the dressing, mix all the ingredients together in a small bowl. Spoon ¼ cup of the dressing over the steaks and marinate for 20 minutes in a cool place. Reserve the remaining dressing.
Put the rice in a saucepan with the stock and lime leaves. Bring to the boil, then cover and simmer for 20 minutes, or according to the packet instructions, until cooked.
Meanwhile, pat the steaks dry with paper towels. Heat a cast-iron chargrill pan or non-stick frying pan over a high heat until hot. Brush with oil, then add the steaks and cook for 2½ minutes on each side for rare meat. Cook for longer if you prefer it medium or well-done. Remove the steaks from the pan and leave to rest for a few minutes.
Place the papayas, cucumber, mint, coriander and red onion in a bowl. Add all but 1½ tablespoons of the remaining dressing and toss gently to mix.
Divide the cooked rice among four plates. Arrange the lettuce leaves on the plates and top with the papaya salad. Slice the beef into strips, arrange on top of the salad and spoon the remaining dressing over the top. Sprinkle with the peanuts, then serve at room temperature.