How to Make It
In a medium saucepan, simmer the honey over moderate heat for 1 minute. Add the kumquats and cook until softened, about 3 minutes. Strain the honey into a medium saucepan; reserve the kumquats separately.
Add the wine and chicken stock to the honey and cook over moderate heat until reduced to 1/2 cup, about 15 minutes. Add the jelly beans, remove the saucepan from the heat and let stand until the sauce has a nice licorice flavor, about 5 minutes. Discard the jelly beans.
Preheat the oven to 350°. In a large saucepan, cover the celery root and potato chunks with water and add 1 teaspoon of salt. Boil over moderately high heat until tender, about 30 minutes. Drain the vegetables; return them to the saucepan and shake over high heat to dry out. Transfer the celery root and potato to a food processor and puree until smooth. Wipe out the saucepan and return the puree to it. Stir in 3 tablespoons of the butter and the hazelnut oil. Season with salt and pepper, cover and keep warm.
Heat a large skillet. Using a sharp knife, score the duck breast skin in a cross-hatch pattern. Season the breasts with salt and pepper and add 3 to the skillet, skin side down. Cook over moderate heat until the skin is deep brown and crisp, about 5 minutes; spoon off the fat once or twice. Turn the breasts and cook until browned on the bottom, about 2 minutes. Transfer the breasts to a baking sheet, skin side down, pour off the fat from the skillet and repeat with the remaining breasts. Bake the duck in the oven for about 6 minutes, or until medium rare. Transfer to a carving board, skin side up, cover loosely with foil and let rest for 5 minutes.
Bring the licorice sauce just to a boil. Remove from the heat and whisk in the remaining 2 tablespoons of butter; season with salt and pepper. Thinly slice the duck breasts crosswise and arrange the slices on 8 large plates. Spoon the licorice sauce over the duck and top with the honeyed kumquats. Spoon the celery root puree alongside the duck and serve.