Place papaya in a large wooden salad bowl. Soften the palm sugar in a microwave oven and mix with the lime juice like a vinaigrette. Add the garlic and sliced chili peppers and pour over the grated papaya. Mix and toss the salad with wooden tongs, but not so heavily that the papaya is broken. This will allow the dressing to penetrate the papaya. It is not as delicate as romaine lettuce. Add the shrimp and peanuts, toss briefly, and serve.
This is an excellent summer salad with no oil. You may reduce the number of garlic cloves and chili peppers to make it less spicy. Also, the tartness of the limes will vary seasonally, so you may need to adjust the amount of palm sugar. This will also affect the amount of fish sauce used, as this dish is supposed to be a balance of sweet, tart, salty, and spicy tastes. White granualted sugar and brown sugar do not substitute, so you will need to purchase palm sugar at an Oriental foods market.