Note: this recipe may not double or triple properly due to many ingredients doing double duty. Also, typically marinades may not be needed in the same quantity when making larger amounts of the recipe.
In a small bowl, whisk 1/2 cup coconut milk, 2 tablespoons lime juice, brown sugar, 2 teaspoons salt, and 2 teaspoons ginger until ginger is dissolved. Transfer to large Ziploc. Add chicken, seal, and massage to coat. Refrigerate for at least an hour and up to five.
Reserve 1/2 cup for drizzling and use the remainder on the salad.
In a small bowl or jar, add peanut butter, sambal oelek, remaining 1/2 cup coconut milk, remaining 2 1/2 tablespoons lime juice, remaining 2 teaspoons brown sugar, remaining 1/2 teaspoon salt, and remaining 1 teaspoon ginger. Blend until smooth.
Add cabbage, carrots, herbs, peanuts, and toasted coconut to a large bowl. Drizzle with peanut sauce and toss.
Preheat grill or grill pan to medium-high (400°F to 450°F)
Oil the grates. If using a grill, cook covered, turning once, until a thermometer inserted in the thickest portion of the chicken reaches 165°F, 3 to 4 minutes per side. If using a grill pan, do not cover. Rest chicken, lightly covered for five minutes, then cut crosswise into 1/2 to 3/4 inch slices.
Transfer salad to a large platter; top with sliced chicken and drizzle evenly with reserved Peanut sauce. Alternatively, serve in individual bowls. Garnish salad with herbs, and serve with lime wedges.
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