A fragrant mixture of ginger and garlic does double duty in this anti-inflammatory dinner -- it amps up the lime dressing and flavors the roasted chicken breasts.
Preheat oven to 425 degrees. In a small skillet, cook ginger and garlic over medium heat in oil, stirring, 1 minute. Reserve 1 tablespoon mixture and transfer remainder to a bowl. Whisk in lime juice and zest and sugar. Season with salt and pepper.
Brush reserved ginger mixture over chicken and season with salt. Roast on a rimmed baking sheet until skin is crisp and a thermometer inserted into thickest parts (without touching bones) reads 165 degrees, about 25 minutes. Let cool slightly, then shred into bite-size pieces (discarding skin and bones).
Toss chicken, cabbage, and carrots with dressing. Season with salt and pepper. Serve, topped with cilantro and cashews.
To grate ginger, we suggest using a ceramic grater for the finest results and the fewest pesky fibrous pieces.