Soak the mushrooms in enough boiling stock to cover them. Set aside and leave to soak for 30 minutes.
Place the tamarind paste into a small bowl and pour in the hot water. Mash paste with fork to extract as much flavor as possible, strain, and reserve the liquid, discarding the pulp.
Soak the chiles in hot water to cover for 5 minutes, drain, reserving the liquid.
In a food processor or blender, process the lemon grass, turmeric, galangal, onion, soaked chiles, and shrimp paste; add a little soaking water from the chiles to form a paste.
Heat the oil in a large, heavy-based pan and cook paste on a low heat for 4-5 minutes. Add the tamarind liquid and bring to a boil, then simmer for 5 minutes. Remove from heat.
Drain the mushrooms, and reserve the stock. Discard the stems, then halve or quarter the mushrooms. Add mushrooms to the pan with their soaking liquid, the remaining stock and jaggery. Simmer for 25-30 minutes or until tender.
Place the rice vermicelli into a large bowl and cover with boiling water, leave to soak for 4 minutes or according to packet instructions.
Drain well and divide among six bowls.
Top with onion and cucumber, then ladle in the boiling shiitake soup. Add some mint leaves to each bowl and serve immediately.