Preheat the grill to medium-high. Pull off and discard any wilted dark green outer lettuce leaves. Cut the head into 6 wedges through the core and put in the freezer for 10 minutes. Whisk the miso, peanut butter, vinegar and ginger together in a small bowl. Whisk in enough warm water to make the dressing pourable, about 4 tablespoons. Set aside. Grill the wedges until just charred, about 2 minutes on each cut side. Transfer to a platter and drizzle with some of the miso dressing.
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