In a bowl or blender, combine olive oil, green onions, garlic, ginger, cayenne, allspice, thyme, paprika, cinnamon, nutmeg, brown sugar, soy sauce, lime juice, salt, and pepper. Mix into a thick marinade.
Rub the marinade all over the chicken, making sure to coat it well and get under the skin if possible. Cover and refrigerate for at least 2 hours, preferably overnight.
Preheat your oven to 375°F. Heat a large oven-safe skillet over medium-high heat and place the chicken skin-side down. Sear for 4–5 minutes until the skin is browned, then flip and cook another 2–3 minutes. Remove chicken and set aside.
In the same skillet, add the rice, chicken broth, coconut milk, salt, and thyme. Stir to combine and bring to a simmer.
Nestle the chicken into the rice mixture, skin-side up. Cover with a lid or foil and transfer to the oven.
Bake for 30–35 minutes until the rice is tender and the chicken is cooked through.
Remove the cover for the last 5–10 minutes to crisp the chicken skin if desired. Let rest for a few minutes before serving.