Soak papaya in a bowl of ice water for 15 minutes. Drain and place in a bowl lined with paper towels to absorb remaining water.
Using a mortar and pestle, pound garlic and chilies until well mashed. Add palm sugar and muddle with the pestle until it turns into a coarse, wet paste. Add peanuts and pound to lightly crush them. Add lime juice and fish sauce and stir with a spoon to dissolve the sugar further.
Transfer the dressing to a larger mixing bowl. Add drained papaya and tomatoes and toss together with the dressing. Press on the tomatoes slightly with the pestle to gently bruise them, until they release a small amount of tomato juice into the salad.
Plate salad and garnish with additional peanuts.