Bring a small pot of water to a boil. Fill a small bowl with ice water. Gently lower the eggs into the boiling water; cook at a boil for 5 minutes. Using a slotted spoon or tongs, immediately transfer the eggs to the ice water to cool. Return the water in the pot to a boil and season with salt.
While the eggs cook, start the green beans.

• Trim the stem ends from the green beans; cut the beans in half on the diagonal.

Add the beans to the boiling salted water and cook until the beans are bright green and just tender, 2 to 4 minutes. Drain.
While the beans cook, make the vinaigrette.

• Pat the steaks dry with a paper towel and season generously with salt and pepper.

In a large frying pan over medium-high heat, warm 1 tablespoon oil until hot but not smoking. Add the steaks and cook, turning frequently, until well browned, 6 to 8 minutes for medium-rare. Transfer to a cutting board to rest for 5 minutes, then cut the steaks across the grain into ¼-inch-thick slices.
While the steaks cook, finish the salad.

• Cut the apple into quarters. Cut away the core, then thinly slice the fruit.
• Juice the lemon.
• Strip the basil leaves from the stems; finely chop the leaves.

In a small bowl, combine the lemon juice and basil with 1 tablespoon oil. Season the lemon-basil vinaigrette to taste with salt and pepper.

• Peel the eggs, then cut them in half.
• Coarsely chop the walnuts.

In a medium bowl, toss the mixed greens with half of the lemon-basil vinaigrette.

Transfer the mixed greens to individual plates. Top with the steaks, green beans, and apple. Drizzle the remaining dressing on top, garnish with the walnuts, and serve.