Pour the vegetable oil into a large heavy-bottomed pot and place the pot over medium heat.
Once the oil is hot, sprinkle the brown sugar into the pot in an even layer.
Allow the sugar to melt and caramelize without stirring. Watch carefully until the sugar reaches a deep brown color.
Carefully add the seasoned chicken to the pot. If using skin-on chicken, place the pieces skin-side down first.
Cook the chicken for 2 minutes, then stir to coat the pieces with the caramelized sugar.
Continue cooking for about 5 minutes, turning occasionally, until the chicken is browned on all sides.
Add the chopped onion, diced carrot, and rinsed pigeon peas to the pot.
Cook over medium heat for 5 minutes, stirring occasionally, until the onion begins to soften.
Add the washed and drained parboiled rice.
Stir until the rice is evenly combined with the chicken, vegetables, and pigeon peas.
Add the chopped cilantro, sliced green onion, whole thyme sprigs, and whole Scotch bonnet pepper.
Cook for 5 minutes, stirring occasionally.
Pour in the coconut milk and chicken stock or hot water.
Scrape the bottom of the pot gently to loosen any browned bits.
Add the remaining 1 tsp salt and additional black pepper to taste.
Stir gently to combine all ingredients. Avoid breaking the Scotch bonnet pepper if a milder flavor is desired.
Reduce the heat to medium-low.
Cover the pot and cook for 20 to 25 minutes, or until the rice is tender and the liquid is absorbed to the desired consistency.
Remove the pot from the heat.
Discard the whole thyme sprigs and the Scotch bonnet pepper, if desired.
Stir in the Golden Ray margarine, if using.
Fluff the rice gently with a fork.
Serve hot or at room temperature.