Preheat a 7 1/4-quart Dutch oven on medium-high heat, then melt butter and add oil. Season chicken generously with salt and pepper and sear until golden on both sides, about 8 minutes. Remove from pot and set aside. Add carrots, onion, celery, and apple, the whole habanero, garlic, bay leaves, and thyme. Season with salt and pepper and saute until they start to soften, about 8 to 10 minutes. Add wine and let reduce by half, scraping up any brown bits remaining on the bottom of the pot. Nestle chicken into pot and add enough broth to almost cover the chicken, about 1 1/2 cups and the gravy sauce. Cover and simmer for 1 hour 45 minutes or until chicken falls off the bone. In the last half hour, remove the lid and let liquid reduce.
To make the gravy: In a medium saucepan, melt butter with oil over medium high-heat. Add giblets and brown on all sides, about 6 minutes. Add onion and continue cooking another 5 minutes, until onions start to soften. Add flour and stir, cooking another 3 to 5 minutes. Whisk in the stock. Bring to a simmer and strain. Discard giblets and put gravy back in the pot. Season with salt and pepper. Keep warm on the stove and add to braised chicken once it's cooked.
Serve Braised Chicken over Coconut Rice n' Peas
Coconut Rice n' Peas:
Heat olive oil in a medium pot over medium-high heat. Add onions and salt and saute, until onion becomes translucent and tender, about 5 minutes. Add rice and saute another 2 minutes to toast rice. Add coconut milk and fill saucepan with enough water to cover the rice by 1/2-inch or measure by placing your thumb tip on the rice and filling the pot with water until the water reaches the middle of your thumbnail. Bring rice to a simmer, cover and cook until rice is tender and liquid has evaporated, about 15 to 17 minutes.
Remove from heat and let rice stand another 5 minutes, covered. Fluff rice with fork and then fold in pigeon peas. Season with salt and pepper, to taste.