Peel the green papaya with a vegetable peeler. Shred using a chef's knife as in the video (or with a mandoline, if you prefer). Slice the carrots into very thin 3-4" pieces.
Shred the dried shrimp by pulsing in a blender until they form a coarse powder.
Roast fresh peanuts in a pan over medium heat. Remove the skins and let cool.
Mix the lime juice and palm sugar together to make a syrup.
Pound Everything Together:
Pound the roasted peanuts until they are broken into halves or quarters. Take them out and set aside for later.
Pound the garlic and then the chilis until completely broken down.
Add the long beans and pound until most are broken open.
Add the tomato halves and pound slightly, just to release the juice.
Add the shredded papaya and pound to mix with the other ingredients.
Add the sliced carrots and pound just enough to incorporate, but not so much that you break the carrot pieces.
Add 2 Tablespoons of the lime juice/palm sugar syrup and 1 Tablespoon of the fish sauce and lightly pound everything together to mix.
Add the shredded dried shrimp and mix.
Taste and adjust the seasonings. You may want to add 1-2 more Tablespoons of the lime juice/palm sugar syrup at this point.
Scoop onto a plate and sprinkle with the chopped roasted peanuts. Enjoy!