To prepare the papaya, julienne the green papaya using a knife or julienne peeler. For extra crunch, soak the papaya in cold water for 5 minutes. Drain well and set aside.
To pound the aromatics, in a mortar, combine the garlic, bird's eye chili, and red finger hot pepper, if using. Pound until coarsely crushed.
To make the dressing, add the palm sugar, fish sauce, and juice from the lime wedges to the mortar. Reserve two lime peels. Pound and mix until the sugar dissolves.
To add the crunchy ingredients, add the reserved lime peels, dried shrimp, half of the roasted peanuts, and green beans. Gently pound a few times to slightly break them up.
To finish the salad, add the papaya and grape tomatoes. Lightly pound and toss until everything is evenly combined and slightly softened.
To serve, transfer the salad to a serving plate and sprinkle with the remaining roasted peanuts. Serve immediately.