Prepare the papaya. Peel the green papaya and shred it using a special shredder or a sharp knife. For a crispier salad, soak the shreds in an ice bath while you prepare the other ingredients.
Make the base. In a large wooden mortar and pestle, add the garlic and chilies. Pound until they are bruised and roughly mashed.
Add the seasonings. Add the palm sugar, Padaek, fish sauce, shrimp paste, and fermented crab paste. Use the pestle to gently mix and combine the ingredients.
Incorporate the vegetables. Add the long beans and lightly bruise them with the pestle. Then, add the halved cherry tomatoes and gently smash them to release their juices.
Combine the salad. Drain the shredded papaya from the ice bath and add it to the mortar. Using a large spoon in one hand and the pestle in the other, toss and gently pound the salad. The goal is to coat the papaya strands with the dressing without turning them into mush. Continue this until everything is well-combined.
Taste and serve. Taste the salad and adjust the flavors as needed, adding more spice, sourness, or a dash of sugar to balance it out. Transfer the salad to a serving plate and enjoy immediately.