Heat oven to 425° F. Combine the vinegar, parsley, chives, dill, and ½ cup of the olive oil in a blender and process until smooth. Transfer dressing to a small bowl, season with salt and pepper, and set aside.
Place 4 cups of the kosher salt in a large bowl. Add 1 cup of water and stir until the salt has the texture of damp sand. Spoon a thin layer of the moistened salt into a 2-quart baking dish. Place the potatoes in the dish, then spoon the remaining salt over top, covering the potatoes and filling in all of the cracks and crevices. Cover the dish with foil and bake until the potatoes are tender, about 45 minutes. When the potatoes are cool enough to handle, dust them off and discard the remaining salt. Slice the potatoes in half and set aside.
Meanwhile, fill a medium saucepan with ¾-inch of water. Bring to a boil over medium heat. Add the eggs and cover. Reduce heat to low and cook for 7 minutes, then remove the pan from the heat. Rinse the eggs briefly under cool water and set aside.
Heat the remaining tablespoon of oil in a large skillet over medium heat. When hot, add the reserved potatoes, cut sides down. Cook until browned and crisp, 6 to 8 minutes. Peel the reserved eggs and slice them in half. To serve, arrange the potatoes and eggs on a platter and spoon the dressing on top.
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