Place potatoes in a medium pot; add cold water to cover.
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 some 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.

Toss green beans, potatoes, tomatoes and spinach in a large bowl with half of the dressing. Arrange on a platter.
Cut eggs into quarters and place eggs and olives in sections on top of salad.
Just before serving, drizzle salad with remaining dressing, then top with fried capers and some dill.

A protein such as seared tuna, cold roasted chicken or smoked trout can be added to make it more substantial.