Select a firm green papaya and shred into thin matchsticks using a shredder or mandolin. Peel and shred the carrot.
In a clay mortar and pestle or a large steel bowl, crush the garlic first. Add and crush the chilies, then add the long beans and continue crushing until well mixed.
Add papaya and carrot. Lightly pound with the pestle while simultaneously using a large spoon to toss the mixture. Continue pounding and tossing until well combined.
Add tomatoes, peanuts, lime juice, soy sauce and sugar. Continue pounding and tossing to mix well and evenly distribute the flavors.
Taste and adjust the flavor with more soy sauce, lime juice and sugar to taste.
Serve with the cabbage or lettuce on the side.