To prepare using a mortar and pestle, combine the garlic, dried shrimp (if using), and chilies in a large, heavy mortar and use the pestle to pound and grind them to a very coarse paste.
Add the papaya and green beans, pounding, scraping, and turning with a spoon now and then, for 1 to 2 minutes, until the papaya shreds are wilting and seasoned and beans are somewhat smashed.
If you do not have a large mortar and pestle, use a rolling pin. Mince the garlic and chilies and place them in a medium bowl along with the dried shrimp. Spread the papaya out on your cutting board, and light into it with the rolling pin for a minute or two, pressing down hard, and mowing back and forth. Stop to gather up the shreds, squeeze them, and spread them out again for another pass or two. When the shreds are wilted, transfer them to the bowl.
Repeat with the green beans, pressing down just until they split open and wilt a bit, and then add them to the bowl.
Add the fish sauce, lime juice, and palm sugar to the papaya and use the pestle to press and grind the mixture a little, and a spoon to turn and mix everything well. Or use your hands to squeeze the mixture a few times and work in the seasonings.
Add the cherry tomatoes and peanuts, toss well, and then mound the salad on a small serving platter, juices and all. Serve at room temperature.