Whisk first 5 ingredients in medium bowl. Set dressing aside. Cook beans in medium saucepan of boiling salted water until crisp-tender, about 5 minutes. Rinse under cold water. Cut into 2-inch pieces. Using julienne peeler, peel enough papaya to measure 6 cups. Place in large bowl. Add tomatoes, cilantro, green onions, chile, and green beans. Pour dressing over; toss. Sprinkle peanuts over and serve. Palm sugar, fish sauce (nam pla or nuoc nam), dried shrimp, Chinese long beans, green papaya, and Thai chiles can all be found at Asian markets.