1. To prepare salad, cook green beans in boiling water 2 minutes or until crisp-tender. Drain and plunge beans into ice water. Drain well.
2. While beans cook, heat a large nonstick skillet over medium-high heat. Add 1 teaspoon oil to pan; swirl to coat. Add potatoes; cook 5 minutes on each side or until browned.
3. While potatoes cook, arrange lettuce and basil evenly on 4 plates. Divide tomatoes, onion, olives, eggs, green beans, and potatoes among plates.
4. Heat skillet over medium-high heat. Add remaining 2 teaspoons oil to pan; swirl to coat. Sprinkle tuna with 1/8 teaspoon salt and 1/8 teaspoon pepper. Add tuna to pan; cook 2 minutes on each side or until desired degree of doneness. Cut thinly across the grain. Arrange tuna on plates.
5. To prepare dressing, combine lemon juice and next 5 ingredients (through garlic) in a small bowl; gradually add 3 1/2 tablespoons oil, stirring constantly with a whisk. Stir in capers. Drizzle evenly over salads.