When buying ripe papayas, look for firm (not hard) fruit with a yellowish rind that has no spots or bruises.
1. Halve 2 papayas and scoop out seeds. Set halves aside. Peel remaining 2 papayas with vegetable peeler, then halve and scoop out seeds. Cut peeled papaya halves into ½-inch dice, and place in medium bowl.
2. Add avocados, cashews, cilantro, lime juice, and shallot to diced papayas in bowl, and toss to combine. Season with salt and pepper. Fold in arugula. Fill papaya halves with salad, and serve immediately.