1. Whisk lime juice, fish sauce, and sugar in a large bowl until sugar dissolves. Transfer 3 tablespoons lime juice mixture to a second large bowl and whisk in 3 tablespoons oil, scallion whites, and 1/4 teaspoon salt to make a dressing; set both bowls aside.
2. Brush cut sides of cabbage evenly with remaining 3 tablespoons oil. Pat chicken dry with a paper towel and season with salt and pepper. Heat grill to high, then clean and oil grates. Grill chicken until it is lightly charred and registers 170 degrees, about 5 minutes per side. Grill cabbage, cut sides down, until lightly charred and wilted, 2 to 3 minutes per side; transfer to a cutting board.
3. Slice chicken, toss with remaining lime juice mixture, and let sit for 10 minutes.
4. Core cabbage and slice crosswise into 3/4"-thick strips. Add cabbage, scallion greens, tomatoes, cilantro, mint, and chili pepper (if using) to bowl with dressing and toss to combine. Season with salt and pepper to taste and transfer to plates. Divide chicken and any accumulated juices over salad, sprinkle with peanuts, and serve.
Source: Hannaford fresh Magazine, May - June 2016