Preheat a BBQ grill or chargrill pan on high. Lightly spray grill with olive oil. Cook steak on the grill for 2-3 minutes each side for medium or until cooked to your liking. Transfer to a plate. Set aside for 10 minutes to rest then thinly slice.
To make the dressing, combine lime juice, fish sauce, ginger, soy sauce and sesame oil in a small bowl and whisk to combine. Set aside.
Place the eggs in a medium bowl and whisk to combine. Heat a non-stick frying pan over medium heat. Lightly spray pan with olive oil. Working quickly, using a whisk, drizzle the pan with a quarter of the mixture back and forth into the pan to form a crisscross pattern. Cook until crisp. Carefully remove and set aside. Repeat with remaining egg mixture, to make 4 egg nests.
Place the cucumber, carrot, red onion, cherry tomatoes, mint, coriander, Thai basil leaves and dressing in a large bowl and toss to coat.
Divide the egg nests between the plates and top with salad, sliced rump steak and peanuts to serve.