Preheat oven to 425°F.
Arrange cabbage wedges on a large rimmed baking sheet. Brush both sides of the wedges with 5 teaspoons sesame oil; sprinkle with ½ teaspoon pepper and ¼ teaspoon salt. Roast until tender and charred, about 20 minutes. Sprinkle with the remaining ⅛ teaspoon salt.
Meanwhile, whisk 2 tablespoons miso, 2 teaspoons each honey and mirin and the remaining 1 teaspoon sesame oil together in a small bowl until combined. Stir in 1 cup yogurt until blended.
Spread the yogurt mixture on a large serving platter; top with the roasted cabbage, 2 tablespoons chili crisp and 1 tablespoon herbs.
