Kosher salt
1 1/2 pounds green beans, trimmed
4 large eggs
1 small shallot, finely chopped
1 teaspoon finely grated lemon zest
1 tablespoon plus 2 teaspoons fresh lemon juice
2 teaspoons Dijon mustard
1 teaspoon honey
1/8 teaspoon freshly ground black pepper
5 tablespoons olive oil, divided
2 tablespoons coarsely chopped dill, divided
1/4 cup drained capers, patted dry
1 bunch breakfast radishes (about 3/4 pound), trimmed, quartered
1/4 cup Niçoise or Kalamata olives, pitted, halved
Place potatoes in a medium pot; add cold water to cover by 1". Season with salt, bring to a boil, and cook until potatoes are fork-tender, 12–15 minutes. Transfer to a large bowl of ice water and chill until cold, about 3 minutes. Transfer to paper towels and pat dry, reserving bowl of ice water. Meanwhile, bring another medium pot of salted water to a boil. Add green beans and cook until crisp-tender, 2–4 minutes. Using a slotted spoon, transfer to ice water; reserve hot water in pot. Chill beans until cold, about 3 minutes. Transfer to paper towels and pat dry, reserving bowl of ice water. Return water in green bean pot to a boil, carefully add eggs, and cook 8 minutes. Transfer eggs to ice water and chill until cold, about 5 minutes. Peel; set aside. Combine shallot, lemon zest, lemon juice, Dijon, honey, pepper, and 1/4 tsp. salt in a medium bowl. Whisk in 3 Tbsp. oil in a slow, steady stream, then whisk in 1 Tbsp. dill. Heat remaining 2 Tbsp. oil in a small saucepan over medium-high. Add capers and cook, swirling pan occasionally, until capers burst and are crisp, about 5 minutes. Transfer capers with slotted spoon to paper towels. Let oil cool. Toss green beans in a large bowl with half of the dressing. Arrange on a platter. Transfer potatoes to same bowl and toss with 1 Tbsp. dressing; arrange in a section on top of green beans. Toss radishes with 1 Tbsp. dressing in same bowl; arrange in another section on top of green beans. Cut eggs into quarters and place eggs and olives in sections on top of green beans, letting some beans show through. Just before serving, drizzle salad with remaining dressing, then top with fried capers and remaining 1 Tbsp. dill.