
Lightly pound the roasted peanuts in a mortar and pestle until they are broken into coarse pieces. Do not crush them into a fine powder. Transfer most to a bowl and reserve some for garnish.
Add the garlic and bird's eye chilies to the mortar and pound until they form a rough paste. Add the dried shrimp and pound a few more times just to break them up and release their flavor.
Stir the palm sugar, lime juice, and fish sauce into the mortar until the sugar is mostly dissolved. Pour the dressing into a large mixing bowl.
Add the snake beans to the mortar in batches if needed. Pound them gently to bruise and soften, then transfer them to the bowl with the dressing.
Lightly crush the grape tomatoes with your hands to release some juice, then add them to the bowl.
Add the shredded green papaya and about three-quarters of the crushed peanuts. Toss thoroughly with tongs or two wooden spoons until the papaya is evenly coated and slightly softened.
Taste and adjust with more lime juice, fish sauce, or chili if needed. Pile the salad onto serving plates, spoon over a little extra dressing from the bowl, and finish with Thai basil leaves and the remaining peanuts. Serve immediately.