In a bowl, whisk the soy sauce, lime juice, sesame oil, ginger and garlic to make the dressing.
Preheat a grill or grill pan to high. Brush the tofu with the oil; season with salt. Grill until grill-marked, about 2 minutes per side. Let cool, then slice each piece into 3 squares. Grill the onions, turning occasionally, until they start to soften, about 5 minutes.
Toss the onion and herbs with half the dressing; divide among plates. Top with the tofu and more dressing; sprinkle with the peanuts.