For the marinade: In a bowl, combine the papaya seeds, garlic, lime zest, lime juice, lemon zest, lemon juice, coconut cream, cilantro, and ginger, and mix thoroughly. Add the chicken breasts to the bowl, and toss to coat in the marinade. Cover the bowl with plastic wrap, and place in the refrigerator to marinate for a minimum of 1 hour or up to 24 hours.
For the chicken: Heat and a grill over medium-high heat and lightly grease the grate with oil. Remove the chicken from the marinade, and lay the breasts on the hot grill. Discard the marinade. Baste each chicken breast with 2 tablespoons Papaya BBQ Sauce, and continue grilling, turning once and basting occasionally with the remaining sauce, until the meat is cooked through. Transfer the chicken to a serving platter and garnish the chicken with the chopped Spiced Cashew Nuts and cilantro leaves, if using.
Heat the oil in a pot over medium heat, and add in the onion. Cook, until the onions are translucent, stirring continuously to ensure the pieces do not brown. Sprinkle the sugar, scotch bonnet, lime zest, and lemon zest over the onions, and stir until the sugar dissolves. Pour in the lime juice, lemon juice, water and vinegar. Bring the ingredients to a boil. Add in the diced papaya, and adjust the seasonings with the salt, if desired. Bring the mixture to a boil again, reduce the heat, and allow the mixture to simmer for 15 minutes. Take the pan off the heat, and let the mixture cool slightly. Carefully transfer the mixture to a blender, and puree the sauce until smooth. Transfer the BBQ sauce to a bowl, and set aside.
In a small frying pan, melt the butter over medium heat. Drop the cashews into the pan, and toast until golden brown. Remove the pan from the heat, then sprinkle over the paprika, and salt, and gently toss to coat.
Reserve the rest of the coconut cream for the Coconut Rice recipe, if serving.