Whisk oil, lemon juice, mustard, honey, pepper, and 1 tsp. kosher salt in a medium bowl; set dressing aside.

Place eggs in a medium pot cover with salted water and bring to a boil. Lower to simmer and cook for 7 minutes. Using a slotted spoon, transfer eggs to a bowl of ice water; chill until cold, about 5 minutes. Peel; set aside.

Meanwhile, add green beans and potatoes to the same pot of boiling water and cook until just tender, 2–4 minutes for green beans, 8-10 minutes for potatoes. Using a slotted spoon, transfer to a bowl of ice water; let sit until cold, about 3 minutes. Transfer to paper towels; pat dry.

To serve, slice eggs in half and arrange on a platter with cooked and raw vegetables and tuna. Top with pickled-briny ingredient(s), sprinkle with sea salt and drizzle some reserved dressing over. Serve with remaining dressing alongside.

Do Ahead: Dressing can be made 5 days ahead; cover and chill. Eggs can be boiled, and vegetables blanched 2 days ahead; cover and chill separately.