Step 1

Whisk lime zest and juice, grated ginger, garlic, coconut palm sugar, fish sauce, ½ cup coconut milk, 2 Tbsp. oil, 2 tsp. pepper in a large bowl to combine. Set ¼ cup marinade aside for serving. Place chicken in remaining marinade and toss to coat. Cover and chill at least 1 hour and up to 12 hours.

Step 2

Preheat oven to 400°. Generously brush cabbage wedges on both sides with oil; season with salt and pepper. Arrange, a cut side down, in a medium cast-iron skillet. Remove chicken from marinade and set, skin side up, on top of cabbage; season with salt and pepper. Roast 35 minutes. Increase oven temperature to 450° and continue to roast, rotating pan halfway through, until chicken thighs are browned and crispy, 5–7 minutes more.

Step 3

Meanwhile, bring rice, ginger slices, remaining 1 cup coconut milk, remaining ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt, and 1 cup water to a boil in a medium saucepan over medium-high heat. Reduce heat, cover, and simmer until liquid is absorbed, 15–20 minutes. Remove pan from heat. Fish out and discard ginger slices. Re-cover pan and let rice sit until ready to serve.

Step 4

Arrange chicken on a platter; drizzle with reserved marinade and top with cilantro leaves. Serve with coconut rice and lime wedges for squeezing over.