Whisk together ½ cup coconut milk, 2 tablespoons lime juice, palm sugar, 1 tablespoon salt, and 2 teaspoons ginger in a small bowl until sugar dissolves. Transfer marinade to a large ziplock plastic bag. Add chicken, and seal bag, pressing out all air. Massage bag to evenly coat chicken with marinade. Refrigerate at least 1 hour or up to 5 hours.
Preheat grill to medium-high (400°F to 450°F). Meanwhile, whisk together peanut butter, sambal oelek, remaining ½ cup coconut milk, remaining 2 ½ tablespoons lime juice, remaining ¾ teaspoon salt, and remaining 1 teaspoon ginger in a large bowl until blended and smooth. Reserve ⅓ cup dressing for drizzling.
Remove chicken from marinade; discard marinade. Place chicken on well-oiled grates; grill, covered, until a thermometer inserted in thickest portion of thighs registers 165°F, 3 to 4 minutes per side. (Alternatively, chicken can be cooked indoors on the stovetop using a grill pan.) Remove from heat; let rest 5 minutes. Slice chicken crosswise into ½- to ¾-inch-thick slices.
Add cabbage, carrots, herbs, peanuts, and toasted coconut to dressing in large bowl; toss until well coated. Season with salt to taste. Transfer cabbage mixture to a large platter; top with sliced chicken and drizzle evenly with reserved dressing. Garnish salad with herbs, and serve with lime wedges.
