Preheat oven to 450°F (232°C) with rack set in lowest position.
Bring a large pot of water to a boil; season generously with salt.
Add 1 pound potatoes and cook until tender, 15 minutes. Using a spider or slotted spoon, transfer potatoes to a baking sheet and let dry briefly.
Add 8 ounces green beans to simmering water and cook 4 minutes. Meanwhile, prepare an ice water bath.
Using a slotted spoon or spider, transfer green beans to an ice water bath, submerge in water and set aside.
Drizzle potatoes with 2 tablespoons oil to coat. Using bottom of a cup, smash potatoes until they are ½-inch to ¼-inch thick. Season with 1 teaspoon kosher salt and ½ teaspoon pepper. Roast until bottoms start to brown, about 15 minutes. Flip and continue to cook until browned and crispy around edges; 10–15 minutes more.
In a large mixing bowl, whisk together remaining 2 tablespoons olive oil, 2 ½ tablespoons mustard, 2 tablespoons vinegar, and ½ teaspoon sugar; season to taste with salt and pepper.
Stir in sliced 1/2 red onion, ¼ cup chopped dill and ½ cup torn olives.
Drain green beans and dry well (I use my salad spinner for this). Cut beans into 1 ½-inch long pieces. Add beans to bowl with dressing and toss to combine.
Arrange potatoes on a large plate or platter. Spoon green bean salad over top. Break 2 (5-ounce) cans tuna into large chunks and nestle on top of salad. Drizzle with olive oil and serve immediately.