Whisk soy sauce, lime juice, chile paste, and peanut oil together in a small baking dish. Add the steaks, turn to coat, cover, and let marinate for 30 minutes in the refrigerator. Remove from the refrigerator 15 minutes before grilling.
Heat grill to high. Remove steaks from marinade and pat dry. Season both sides with pepper and grill for 3 minutes per side or until slightly charred and cooked to medium-rare doneness. Remove from the grill, let rest 5 minutes, and slice into 1/4-inch thick slices.
While steak is resting, combine all salad ingredients in a large bowl. Toss with half of the dressing and season with salt and pepper. Transfer to a platter, top with the steak, and drizzle the remaining dressing over the top.
Whisk ingredients together in a small bowl. Season with salt and pepper, to taste. Let sit 10 minutes before using.
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