1. Combine shallot, vinegar, and 2 teaspoons oil in a bowl. Add green beans and toss well. Season with salt and pepper; set aside. Combine potatoes, 1 tablespoon oil, and dill and toss well. Season with salt and pepper; set aside. Combine corn, 1 tablespoon oil, and cheese and toss well. Season with salt and pepper; set aside.
2. Bring a small pot of water to a boil. Add basil and cook 30 seconds. Transfer with a slotted spoon to a bowl of ice water to stop the cooking. Squeeze basil dry, then transfer to a small food processor or mortar and pestle. Add remaining 3 tablespoons oil and 1/2 teaspoon salt. Puree until smooth. Toss basil oil with tomatoes and season with salt and pepper; set aside.
3. Arrange endive, salmon, shrimp, sausage, lettuce, eggs, and basil leaves on a platter. Add dressed green beans, potatoes, corn, and tomatoes. Serve with anchovies and olives.
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