How to Make It
In a large pot, bring 16 cups of water and 1/2 cup of salt to a boil with the crushed ginger and halved scallions. Add the chicken and remove from the heat. Cover and let stand until cooked through, 35 minutes.
Meanwhile, in a saucepan, heat 2 tablespoons of the oil until shimmering. Add the garlic and cook over moderately high heat, stirring, until golden, 2 minutes. Add the red pepper, five-spice powder and sliced scallions and cook, stirring, until softened, 3 minutes. Add the stock, black-bean and soy sauces and bring just to a boil. Whisk in the cornstarch mixture and cook until the sauce is thickened, 2 minutes. Stir in the 1/2 teaspoon of grated ginger with the sesame oil and the 1 teaspoon of vinegar; keep warm.
In a bowl, toss the pear, mandarins, basil and cashews with the remaining 1 tablespoon each of oil and vinegar and season with salt.
Transfer the chicken to a carving board and discard the skin and bones. Slice the breasts crosswise, transfer to plates and drizzle with some of the sauce. Serve with the salad, passing additional sauce at the table. make ahead The sauce can be refrigerated overnight; reheat gently, adding water if it is too thick.