- Pick through the crab for bits of shell and cartilage. Put meat in a glass bowl, add the onion, celery, and 2 tablespoons capers. Gently toss until evenly mixed.
- Cut the lemon in half and squeeze the juice from one of the halves over the crab. Add 2 tablespoons of mayonnaise and a pinch of cayenne. Toss gently until the mayonnaise is very lightly coating the crab. It should still be loose and crumbly, but if it’s too dry, add just enough to make a very light coating but no more than a tablespoon. Taste for lemon juice, cayenne, capers, and salt, adding more of each as needed. Cover and refrigerate until you are ready to serve, at least 1 hour. It can be made as much as 6 hours ahead.
- Just before serving, tear the basil leaves into very small pieces and add them to the salad. Toss gently and taste one last time, adjusting the cayenne and salt if needed. Transfer to a serving bowl and serve immediately.