For the chicken: Preheat the oven to 350 degrees F. Spread the garlic cloves onto a sheet tray and roast, 20 minutes.
Set up a deep fryer with canola oil and heat to 350 degrees F. Fry the brussels sprouts until crispy, 3 to 4 minutes. Remove to a paper towel-lined plate. Season with salt.
Lower the temperature on the fryer to 275 degrees F.
Combine the cornstarch, baking powder and salt to taste in a wide shallow dish. Dredge the chicken halves in the cornstarch mixture and shake off any excess. Deep-fry the chicken for 10 minutes, then remove from the oil onto a paper towel-lined tray.
Increase the temperature on the fryer to 400 degrees F. Place the chicken back into the fryer to crisp for 5 minutes, or until it reaches an internal temperature of 165 degrees F.
Add 1/4 cup each of the apple cider and apple cider vinegar to a large saute pan placed over medium-high heat. Allow to reduce by half, about 5 minutes. Add half the chicken stock and salt to taste. Reduce by half, about 5 minutes, then add the remaining chicken stock. Add the roasted garlic and allow the sauce to reduce, 5 to 7 minutes. Finish the sauce with the remaining 2 tablespoons each apple cider and apple cider vinegar and the butter.
For the dirty rice: Add the onion, salt to taste and 2 tablespoons of the extra-virgin olive oil to a medium saucepan and turn the heat to medium high. Sweat the onion until translucent, 5 to 7 minutes. Add the rice and stir to coat. Toast for 2 to 3 minutes. Add the chicken stock, bay leaves and salt to taste. Bring to a boil, cover, reduce to a simmer and cook until the rice is tender, 15 to 20 minutes. Fluff with a fork and set aside.
Heat a large saute pan with the remaining 2 tablespoons extra-virgin olive oil over medium-high heat. Add the shallot and salt to taste. Saute until translucent, 5 minutes. Add the chicken livers and blood sausage and brown until cooked through, 4 to 5 minutes. Add the cooked rice to the pan and stir to combine, tossing to thoroughly coat the rice in the chicken livers and blood sausage. Remove the pan from the heat, add the brandy and ignite with a click lighter. Put the pan back on the heat and cook for 2 to 3 minutes until the alcohol has cooked off. Turn off the heat and stir in the scallions.
For the glazed carrots: Season a pot of boiling water generously with salt. It should be as salty as the sea. Prepare an ice bath and season generously with salt. Add the carrots to the boiling water and cook for 2 to 3 minutes until tender but still slightly crisp. Remove the carrots and immediately plunge into the ice bath. Set aside.
Melt the butter, brown sugar and cayenne together in a large saute pan over medium-high heat. Add the chicken stock and the blanched carrots. Toss to coat the carrots, then allow the liquid to reduce until the glaze has thickened, 5 minutes. If the mixture needs to be thinned out, you can add a bit more chicken stock.
To plate: Place a scoop of dirty rice onto the plate. Top with the glazed carrots, followed by the chicken. Spoon the sauce over the chicken, making sure to include the roasted garlic cloves. Garnish with the crispy Brussels sprouts and micro radish.
Use extreme caution when igniting alcohol. Remove the pan from the heat source before adding the alcohol. Pour the alcohol into the pan and carefully ignite with a match or click lighter. Return the pan to the heat and gently swirl to reduce the flames.