Blanch garlic in a large saucepan of boiling water for 3 minutes. Transfer garlic to a food processor or blender; set aside. Add beans to boiling water and cook 4 minutes, or until crisp–tender. Remove beans, rinse under cold water and drain. Add potatoes to pan and cook 12 minutes, or until tender; drain.
Add vinegar, mayonnaise, oil and salt to garlic in food processor and purée. Add basil and 2 tablespoons water and purée again.
Transfer dressing to a large bowl. Add tomatoes, beans, potatoes and tuna, tossing to coat. Tear lettuce into small pieces. Add lettuce and toss again. Garnish with olives.
Remarkably lean for a fish with so much flavour, tuna provides good amounts of healthy omega-3 fatty acids. It is also an excellent source of some B vitamins.