Whisk the peanut oil, soy sauce, sherry vinegar and rice vinegar together in a bowl.
In a large casserole or other shallow dish, pour the marinade over the tofu slices. Turn over to coat all the slices. Place in the refrigerator for about 3 hours, turning the tofu slices about 4-6 more times.
Brush an indoor grill lightly with a nonstick spray and heat up to high (or sear setting). Lift each slice of tofu out of marinade to briefly drain and arrange on grill. Grill for about 3 minutes, then turn over to cook another 4 minutes more. Remove from grill, and serve with the slaw and sesame dressing.
Combine the sliced cabbage, bean sprouts, green onion, cilantro, edamame and peanuts in a large mixing bowl. Toss well to incorporate ingredients.
In a small mixing bowl, whisk the sherry vinegar, rice vinegar, dark sesame oil, peanut oil, soy sauce, sugar and grated gingerroot together. Add in a pinch of white pepper to taste.
Pour over the salad ingredients and toss well to coat the slaw. Serve with the grilled tofu.