1Prepare the green papaya. Choose a firm, unripe papaya that is completely green with no yellow spots - ripe papaya is too soft and sweet for som tum. Peel the papaya with a vegetable peeler, then cut it in half lengthwise and scoop out the seeds. Shred the papaya using the large holes of a box grater, a julienne peeler, or the traditional method of scoring the flesh with a knife and then shaving off thin strips. You want long, thin shreds about the thickness of matchsticks. Alternatively, you can use a food processor with a shredding disc. Place the shredded papaya in cold water until ready to use to keep it crisp. You should have about 3 cups of shredded papaya.
2Prepare the remaining ingredients. Cut the long beans into 1-inch pieces - long beans are traditional but green beans can be substituted. Halve the cherry tomatoes. Measure out the dried shrimp and roasted peanuts. Make the dressing by combining the fish sauce, palm sugar, lime juice, and tamarind paste if using in a small bowl. Stir until the sugar dissolves. The dressing should taste balanced - sour, salty, and sweet in equal measure with sour being slightly dominant. Adjust to your taste. Traditional som tum is made to order with seasonings added directly to the mortar, but preparing the dressing separately works well for home cooking.
3Using a large mortar and pestle (Thai clay mortar called krok is traditional), add the garlic and Thai chilies. Pound them together until roughly broken down but not completely pulverized - you want some texture remaining. The number of chilies determines the heat level: 3 chilies is mild to medium, 4-5 is hot, and 6 or more is Thai spicy. Add the dried shrimp and pound a few more times to break them up slightly and release their flavor. Add the peanuts and pound just enough to crack them - you want chunky pieces, not powder.
4Add the long beans and tomatoes to the mortar. Pound and bruise them gently using a combination of pressing and light pounding - the tomatoes should release some juice but not turn into mush, and the beans should be slightly bruised to absorb the dressing. The pounding motion should be more of a pressing and turning action rather than aggressive smashing. If you do not have a mortar and pestle large enough, you can bruise the vegetables in a large bowl using the end of a rolling pin or a wooden spoon, or simply skip the bruising and mix everything in a bowl for a less traditional but still delicious version.
5Drain the shredded papaya well and add it to the mortar. Pour the prepared dressing over the papaya. Using the pestle in one hand and a large spoon in the other, pound and toss the salad repeatedly. The technique involves pounding down with the pestle while simultaneously turning and lifting the ingredients with the spoon. This action bruises the papaya slightly, helping it absorb the dressing while maintaining its crunch. Continue for 1-2 minutes, tasting as you go. Adjust the seasoning if needed - add more lime for sourness, more fish sauce for saltiness, more sugar for sweetness, or more chilies for heat. The flavors should be bold and well-balanced.
6Transfer the som tum to a serving plate, scraping out all the delicious juices from the mortar. The salad should look vibrant with green papaya, red tomatoes, and visible peanuts and dried shrimp. Serve immediately while the papaya is still crisp and the flavors are fresh. Som tum is traditionally served with sticky rice - tear off small pieces of sticky rice and use them to scoop up the salad. Fresh cabbage wedges are also served alongside for scooping and to provide a cooling contrast to the spicy salad. Grilled chicken (gai yang) or grilled pork neck (kor moo yang) are classic accompaniments for a complete Isan meal. Som tum is best eaten immediately and does not store well as the papaya will soften and release water.