How to Make It
In a small skillet, combine 1 cup of the peanut oil with 4 teaspoons of the crushed red pepper and cook over moderate heat, swirling the skillet until the pepper is sizzling, about 2 minutes. Pour the seasoned oil into a large glass baking dish and add the smashed ginger, garlic and orange zest. Let cool slightly, then add the sesame oil, five-spice powder and 1 tablespoon plus 1 teaspoon of the lemon juice. Add the chicken breasts and turn to coat. Cover and refrigerate overnight.
In a small bowl, combine the remaining 1/4 cup of lemon juice with the grated ginger, shallot, brown sugar and the remaining 1 teaspoon of crushed red pepper. Whisk in the remaining 1/2 cup of peanut oil until emulsified. Season the vinaigrette with salt and pepper.
Preheat the broiler and position a rack 8 inches from the heat. Drain the chicken breasts, scraping off most of the marinade but leaving on some of the crushed red pepper, and transfer to a baking sheet. Broil the chicken for about 35 minutes, turning frequently, until golden and cooked through. Transfer the chicken to a platter and let cool. With your fingers, pull the chicken apart into large pieces and add to a large bowl. Pour any accumulated cooking juices into a bowl and spoon off the fat.
Add the reserved juices and half the vinaigrette to the chicken, toss well and refrigerate until chilled, about 30 minutes. Fold in the papaya and season with salt and pepper.
In another large bowl, toss the greens with the mint, basil and remaining vinaigrette. Season with salt and pepper and transfer to plates or a large platter. Mound the chicken and papaya salad on the greens and serve immediately.