Bring a large pot of water to a boil. Add 1 tablespoon salt, then green beans, and cook until just
tender, 3 to 4 minutes. Drain and rinse under cold water to cool.
Meanwhile, in a blender, puree shallot, basil, oil, vinegar, and 1/2 teaspoon each salt and
pepper until smooth.
Transfer half of dressing to large bowl and toss with green beans. Fold in lettuce, white beans,
and tuna and serve with remaining dressing and eggs.