Place coconut milk, ginger, garlic and lemongrass in a saucepan. Heat on medium until just at simmering point. Remove from heat and set aside for 30 minutes, until flavours infuse. Strain and discard flavourings.
Preheat a chargrill or barbecue on high. Thread each prawn onto a soaked bamboo skewer, tail end first, and brush liberally with coconut milk mixture. Cook for 2 minutes each side, brushing with coconut milk, until prawns are opaque.