Arrange crab claws in grill wok or on layers of heavy-duty aluminum foil pierced evenly with sharp knife. Drizzle crab claws evenly with 1 tablespoon of the oil and sprinkle with 1/2 teaspoon of the pepper.
Grill claws over medium-high heat 5 minutes or until thoroughly heated. Remove from grill.
For sauce, whisk together remaining 3 tablespoons olive oil, remaining 1/4 teaspoon pepper, salt, lemon juice, mustard, tarragon, onions and parsley. Crack open claws and serve immediately with sauce.
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