For 4 Person(s)
Clean the lemongrass stalks by removing and trimming dried hard root and brown leaves, reducing to clean stalks about 6 inches long including the bulbous base. Using the blunt edge of a cleaver blade or the side of an unopened can, bruise each stalk by whacking it firmly at 2-inch intervals and rolling it over to bruise on all sides. Cut into 2-inch lengths.
In a large saucepan combine the coconut milk and vegetable stock, and bring to a gentle boil over medium-high heat. Stir in the lemongrass, galangal, peppercorns, and half of the lime leaves; adjust the heat to maintain an active simmer.
Cut the squash into bite-sized (peeled) pieces; you should have 3 to 4 cups. Add to the simmering soup along with the mushrooms. Increase the heat to medium-high and bring soup back to a gentle boil. Cook for 10 minutes. Add the tofu and cook until the squash is tender but still firm and the tofu is heated through, about 5 minutes longer.
Remove the soup from the heat and use tongs to remove and discard the lemongrass, galangal or ginger, and lime leaves. Stir in the soy sauce, salt, lime juice, cilantro, green onions, and the remaining lime leaves. Taste and add more salt, soy sauce, or lime juice if you like. Transfer to a serving bowl and serve hot.