In a small skillet, toast the whole spices over moderate heat for 1 minute. Let cool completely, then coarsely grind.
In a large, shallow baking dish, mix 1 tablespoon plus 2 teaspoons of the ground spices with 2 tablespoons of the olive oil, the port, garlic, turmeric, 1/4 teaspoon of salt and 1/2 teaspoon of pepper. Add the chicken breasts and turn to coat. Cover and refrigerate for 2 hours or overnight.
Mix the remaining ground spices with the lemon juice, shallot and the remaining 3 tablespoons of olive oil and season with salt and pepper.
In a saucepan of boiling salted water, cook the green beans for 3 minutes. Drain and refresh under cold water. Pat dry and cut into 2-inch lengths.
Light a grill or preheat a grill pan. Remove the chicken breasts from the marinade; discard the garlic. Grill the chicken over moderately high heat until cooked through, about 4 minutes per side. Let rest for 5 minutes, then cut in to 1 1/2-inch chunks.
In a large bowl, toss the lettuce with the papaya, tomatoes, green beans, chicken and the dressing. Sprinkle with the cashews and serve.