For the duck: Rub the duck with the olive oil, season it well with salt and pepper and place in a roasting pan breast-side up. Roast for 15 minutes, then shake the pan to release the duck and roast another 25 minutes. At this point, turn the duck onto the breast so it can baste in its own rendered fat. Roast another 25 minutes, then turn the duck again onto its back and cook for another 15 to 20 minutes. The duck skin should be golden brown and a thermometer placed in the thigh meat should register an internal temperature of 135 degrees F. Remove the duck from the pan, reserving the fat in the pan. Let the duck rest for 10 minutes, then slice into 8 pieces: 2 legs, 2 thighs, 2 wings and 2 breasts.
For the Cabernet sauce: In a medium skillet over medium heat, heat the olive oil. Add the duck neck and chicken thighs, skin-side down, and saute until golden brown and the fat has rendered, about 10 minutes.
Meanwhile, in a large skillet over medium heat, add the butter followed by the onions, garlic and shallots. Saute until translucent, 5 to 6 minutes. Add the cognac and cook for 2 to 3 minutes. Add the Cabernet Sauvignon and bring to a simmer. Add the duck neck, chicken thighs, bay leaves, sage, thyme, parsley, chives and chicken stock. Bring to a simmer and cook, uncovered, for 20 minutes.
For the mushroom ragu: In a heavy saucepan over medium heat, add 2 tablespoons of the butter. Add the mushrooms and cook gently for 7 to 8 minutes; season with sea salt and cracked black pepper. Then add the sherry, garlic, onion and half of the scallions and cook for 4 minutes. Add the ginger, 2 tablespoons butter and the remaining scallions and cook another 2 to 3 minutes. Set aside.
For the radishes: Put the radishes in a pot and cover with cold water. Bring to a boil, add salt and cook until the radishes are just tender. Drain.
In a separate saucepan over medium heat, add the poached radishes and 1 tablespoon of the rendered duck fat and saute until golden, 7 to 8 minutes. Check for seasoning.
For serving: Preheat the oven to 300 degrees F.
Reheat the duck meat on a sheet tray until warmed through, about 4 minutes. Place the mushroom ragu and radishes on a platter. Cut each breast into four pieces and place on a platter with the thighs and legs. Top with the Cabernet sauce.