Combine the tahini, lemon juice, garlic, cumin, salt and cayenne in a jar with a tight-fitting lid and shake well. Measure the oil reserved from the tuna and add additional olive oil to make ?1/3 cup. Add the oil to the jar and shake well again. Set aside.
Combine the tuna, fennel, onion, tomatoes, olives and parsley in a mixing bowl. Drizzle half the dressing over it and toss gently. Serve the salad mounded on lettuce leaves, and pass the remaining dressing separately.
Note: The dressing can be prepared up to 2 days in advance and refrigerated, tightly covered.
Variation: Add 1/4 pound cooked and chilled small pasta such as macaroni or small shells to the salad. If adding pasta, increase the amount of dressing made by half.