Shred the papaya in a food processor.
Put the green beans in a large bowl and bruise them lightly with a wooden spoon. Add the tomatoes, scallions, chile pepper and the papaya.
Stir the fish sauce, brown sugar, lime juice and a pinch of salt together in a small bowl, then add it to the papaya mixture and toss to coat. Toss in the cilantro. Let stand 15 minutes. Toss in the peanuts, if using, right before serving.