Pick over the crabmeat for any bits of shell and put it in a bowl. Refrigerate until just before serving.
Sliver the scallions, both the white and pale green parts. Pick the leaves from the parsley. If the leaves are small and tender, leave them whole; otherwise, sliver them. Separate and trim the leaves of the endive. Zest a teaspoon or so of the lemon.
To assemble the salad, squeeze half the juice of the lemon over the crabmeat. Add the lemon zest, scallions, and parsley and season lightly with salt and pepper. Drizzle with the sesame oil and toss very gently. Taste and adjust the seasoning with more lemon juice if necessary.
Pile the crab salad into a platter. Surround with the endive leaves. Serve immediately.