Step 1
In a large mortar and pestle, pound the shrimp until coarsely ground; transfer to a small bowl and set aside. To the mortar, add the chiles, garlic, and shallot and pound until bruised. Working in batches, add the mangoes and pound, using a spoon to scrape the sides and combine well after each batch, until the fruit is softened slightly and fully coated in the aromatics. Transfer the mixture to a large bowl and set aside.
Step 2
To the mortar, add the green beans and tomatoes and lightly pound to extract their juices. Stir in the fish sauce, lime juice, and sugar, then transfer to the bowl with the mango mixture and toss well. Transfer to a serving bowl or platter, garnish with the crushed dried shrimp and peanuts, and serve at room temperature.