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.
STEP 2
Meanwhile, in a blender, puree shallot, basil, oil, vinegar, and 1/2 teaspoon each salt and pepper until smooth.
STEP 3
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.