1. Combine sour cream, mayonnaise, buttermilk, vinegar, parsley, mustard, sugar, 1/2 teaspoon salt, and 1/8 teaspoon pepper in medium bowl. Set aside.

2. Place cabbage and radicchio on rimmed baking sheet and brush with oil (do not clean sheet). Grill over hot fire until lightly charred and beginning to wilt, 2 to 4 minutes on each cut side. Return to sheet and let cool, 5 minutes. Slice cabbage and radicchio thin, then transfer to bowl with reserved sour cream mixture. Toss to combine and season with salt and pepper to taste.

Makes about 3/4 cup