Step 1In a medium bowl, combine the shallots, garlic, lemon juice, vinegar and kosher salt. Add the oil, whisking it in a slow, steady stream to combine. Stir in the herbs and pepper. This makes about 1 cup vinaigrette.
Step 1Prepare the wax beans: Bring a pot of salted water to boil and prepare an ice bath. Cook the wax beans to al dente (they should still be crisp but cooked), 1 to 2 minutes, then drain and chill in the ice bath to stop the cooking. Remove and pat dry. Trim the stem from the beans, leaving the tails. Slice the beans on the extreme bias into very long pieces using a Frencher or a knife. Set aside.
Step 2To prepare the potatoes, steam them until they are tender when pierced with a small sharp knife, about 20 minutes. Set aside until cool enough to handle, then peel (discard the skin) and slice into one-half-inch thick rounds. Set aside.
Step 3To soft-cook the eggs, bring a saucepan of salted water to boil and gently drop in the eggs, in their shells. Boil for about 7 minutes, or until the yolk is just set (it should not be close to being hard-boiled). Remove the eggs and drop in an ice bath to chill. Carefully peel the chilled eggs, then halve each lengthwise. Set aside.
Step 4To prepare the crostone, heat the oven to 350 degrees, or heat a sandwich press. If using the oven, place the bread slices on a baking sheet, brushing the tops with oil, and bake until golden brown and crisp, 15 to 20 minutes. If using a sandwich press, brush both sides of the bread with olive oil and toast. Remove the crostone and rub the oiled sides lightly with garlic.
Step 5To assemble the salad: In a large mixing bowl, combine the wax beans, potatoes and olives. Season as desired with salt, and dress with vinaigrette to taste. Pile the bean salad on the side of each of 6 plates, making sure the potatoes and olives are equally dispersed among the servings. Set the crostone next to it, spooning the well-stirred bagna cauda over the bread, and sprinkle with sliced parsley. Top with one-half soft-cooked egg and then an anchovy fillet. Grate the bottarga over the beans and serve immediately.