Pull off the top shell of the crab, discard the lungs, and wash well.
Remove the claws, halve the body, and crack the claw shells with a cleaver.
Heat the vegetable oil to 180°C in a large wok.
Stir-fry the crabmeat for 2 minutes then drain on kitchen paper.
In a clean wok, boil the coconut cream until the fats separate.
Fry the chilli paste and lime leaves in the cream until fragrant.
Caramelise the palm sugar in the mixture and stir in the fish sauce.
Add coconut milk, bring to a boil, then simmer the crab in the sauce for 6 minutes.
Finish the dish by stirring in the Thai basil and lime juice.