Cut Scotch bonnet chile in half. Chop half; reserve both halves. (Chile pepper is very hot, so use gloves when chopping, and avoid touching your eyes, nose, or mouth after chopping.) Cut chicken into large chunks.

Heat olive oil in a large skillet or Dutch oven over medium heat. Add chicken; brown on all sides, about 15 minutes. Stir in chopped Scotch bonnet, onion, and garlic. Cook, stirring occasionally, until onion is translucent, about 5 minutes.

Add rice; stir to coat with oil. Cook until rice turns slightly opaque but doesn’t brown. Add chicken broth; bring to a boil over medium heat, then reduce heat to a simmer. Simmer for about 5 minutes; stir in black-eyed peas, coconut milk, green onions, and thyme until well combined. Lay cabbage chunks on top of rice mixture; place remaining Scotch bonnet half on top of cabbage.

Cover the skillet; simmer until rice and cabbage are tender, about 20 minutes, checking occasionally to see if mixture is getting too dry on the bottom (add a small amount of water if needed to prevent burning). Stir in butter; season with salt and black pepper.