How to Make It
Cut the meat from the chicken legs. Cut the meat and any skin into 1-inch pieces; reserve the bones. Season the meat with salt and pepper.
In a medium skillet, heat the oil. Add the chicken bones and meat and cook over high heat, stirring occasionally, until richly browned, about 6 minutes. Add the onion and carrot and cook, stirring, until browned, about 4 minutes. Add the wine and boil until reduced to 2 tablespoons, about 2 minutes. Add 1 cup of water and boil until reduced by two-thirds, about 3 minutes. Add another 1 1/2 cups of water and simmer over low heat until reduced to 1 cup, about 25 minutes. Strain the stock into a small saucepan. Skim off the fat and boil the stock over high heat until reduced to 1/3 cup, about 3 minutes.
In a small skillet, cook the butter over moderate heat until nutty brown, about 2 minutes. Pour the brown butter into the chicken jus.
Preheat the oven to 350°. In a pie plate, toast the walnuts for about 6 minutes, until golden. Let cool, then break them in half.
Cut the skins and bitter white pith from the mandarins, grapefruit, orange and lemon. Cut in between the membranes to release the sections into a bowl. Cut the grapefruit, orange and lemon sections in thirds.
Arrange the citrus pieces on plates along with the walnut pieces, ginger slices and kumquat. Scatter the lettuce, radicchio and herbs around the plate. Bring the brown butter chicken jus to a simmer, whisking, and season with salt, pepper and cayenne. Drizzle the brown butter sauce over the citrus and garnishes and serve right away.
The brown butter chicken jus can be refrigerated overnight. Reheat gently.