Combine 3 Thai chiles, stems removed, 6 garlic cloves, ¼ cup dried shrimp, and ¼ cup granulated coconut palm sugar or 1.5 oz. whole coconut palm sugar, coarsely chopped, in a mortar and pound with pestle until sugar dissolves slightly and chiles, garlic, and shrimp are crushed to a textured paste, 1–2 minutes.

Cut 1 lime into eighths to make wedges. Squeeze juice of 3 wedges into mortar and pestle, then add juiced wedges. Set remaining 5 wedges aside. Add ¾ cup cherry tomatoes (about 4 oz.) and pound to smash lime wedges and break up tomatoes, 1–2 minutes.

Add 2 Tbsp. fish sauce, 2 Tbsp. fresh lime juice, and one fourth of 1 lb. green beans, trimmed, cut into 2" pieces, and pound until green beans break up slightly. (There should be a significant amount of juice at this point.) Add remaining beans a handful at time, pounding after each addition and transferring to a large bowl as you go if needed, until all of the green beans are broken up.

Add ¼ cup salted dry-roasted peanuts and smash just to lightly crush. (Do not over-grind; it will give the salad a mealy texture.) If working in batches, mix everything together in bowl.

Taste som thum and add more palm sugar if needed. Squeeze in juice from reserved lime wedges to taste. Transfer som thum to a large shallow bowl and top with chopped salted dry-roasted peanuts if desired. Serve with cabbage wedges and sticky rice if desired.