Preheat the oven to 350 degrees F (175 degrees C). Place peanuts on a baking sheet.
Toast in the preheated oven until fragrant and browned, 7 to 8 minutes. Let cool for 5 minutes.
Grind roasted peanuts, Thai chilies, garlic, dried shrimp, and sugar in a mortar and pestle or food processor. Stir in lime juice and fish sauce to make dressing.
Toss papaya, tomatoes, green beans, and carrot with dressing. Season with salt and pepper.
Make sure to use a green papaya. You can use palm sugar instead of white.
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