Preheat broiler.

Combine 2 teaspoons oil and 1 teaspoon mustard; brush evenly over fish. Broil fish 3 minutes on each side or until fish flakes easily when tested with a fork.

Cut fish into 1-inch pieces; set aside.

Place green beans in a saucepan; add water to cover. Bring to a boil, and cook, uncovered, 3 to 4 minutes or until crisp-tender; drain.

Combine vinegar, remaining 2 teaspoons mustard, dill, salt, and pepper. Add 2 teaspoons oil, stirring well with a whisk.

Combine green beans, onion, tomato, and tuna in a small bowl; toss gently. Combine 1 tablespoon vinegar mixture and cannellini beans. Arrange lettuce on a serving platter. Arrange bean mixture over lettuce, and top with tuna mixture. Drizzle remaining vinegar mixture over salad.