Heat oil in a saute pan. Add onion and celery and saute until onion is translucent. Remove from heat and set aside.
In a large bowl, mix crabmeat, coconut, mayonnaise, mustard, chives, parsley and 1 cup panko with the onion/celery mixture. Add salt and pepper, to taste. Form into 2-inch diameter cakes.
Roll cakes first in flour, then in beaten eggs, then in the remaining 4 cups of panko, each time shaking off excess. Heat oil, and saute the crab cakes until golden brown. Drain on paper towels. Arrange on a platter and garnish with tomatoes and chives. Serve with coconut basil mayonnaise.
Combine all ingredients in a mixing bowl, and whisk until smooth. May be prepared a day ahead, covered and refrigerated. Bring to room temperature before serving.