Grill the chicken: Rub chicken with olive oil and season with spices. Grill over medium heat for about 5–7 minutes per side, or until cooked through. Set aside to rest.
Make the slaw: In a large bowl, combine shredded cabbage, carrots, mango, herbs, and green onions.
Whisk the dressing: In a small bowl, mix olive oil, vinegar or lime juice, sweetener (if using), salt, and pepper. Pour over the slaw and toss well.
Slice the chicken: Once cooled slightly, slice the chicken thinly.
Assemble: Serve the slaw topped with grilled chicken slices. Garnish with extra herbs or a wedge of lime if desired.