Step 1: Prepare the Peanuts
Place peanuts in a mortar and pestle and lightly pound them to break into large pieces. (Do not grind into a powder.)
Transfer to a bowl and set aside.
Step 2: Make the Garlic & Chili Paste
In the mortar, pound the garlic and chilies into a rough paste.
Add dried shrimp and pound lightly to crush them. (No need to make a fine paste.)
Step 3: Prepare the Dressing
Stir in palm sugar, lime juice, and fish sauce into the garlic-chili mixture until the sugar dissolves.
Pour the dressing into a large mixing bowl.
Step 4: Bruise the Snake Beans
Add the snake beans to the mortar (in batches if needed).
Pound them lightly to soften and split them. (Since they are raw, bruising helps them absorb the dressing.)
Add to the bowl with the dressing.
Step 5: Crush the Tomatoes
Take handfuls of grape tomatoes, lightly crush them with your hands, and add to the bowl.
Step 6: Assemble the Salad
Add the shredded green papaya and ¾ of the peanuts to the bowl.
Toss everything well using wooden spoons or tongs until evenly coated.
Step 7: Serve & Garnish
Pile the salad onto serving plates.
Spoon over any extra dressing from the bowl.
Garnish with Thai basil leaves and the remaining peanuts.
Serve immediately (see Notes).