In a small bowl, cover the dried shrimp with hot water. Let stand for 5 minutes, then drain. Cut the shrimp into thirds.
Using a serrated knife, halve the papaya crosswise and peel the skin. Scrape out the seeds. Using a mandoline, julienne the flesh (you should have about 6 cups).
In a large mortar, pound the chiles to a coarse paste with the garlic. Add the sugar and shrimp and pound until blended. Add the green beans and lightly pound them. Pour in the lime juice and fish sauce and stir to dissolve the sugar. Add the tomatoes and lightly pound them. Scrape the mixture into a large bowl. Add the papaya and peanuts, toss well and serve.