Place the ginger, lemongrass, kaffir leaves, shallot and chillies into a pan with the coconut milk and heat, stirring.
Cook for 5 minutes, then add the mushrooms and bring just below the boil.
Heat for another 5 minutes, season and add lime juice and fish sauce.
Add the coriander and lime zest and serve with the noodles, lime wedges and chilli slices on the side.