2 medium (or 1 large) shallots, minced
1/4 cup fresh lemon juice
1/4 cup Dijon mustard
2 tablespoons rice wine vinegar
Salt and ground black pepper
1 cup plus 3 tablespoons extra-virgin olive oil
2 1/4 to 2 1/2 pounds fresh tuna steaks, cut into 8 pieces
16 small red new potatoes (2 1/4 pounds), halved
8 plum tomatoes, halved lengthwise
1 1/4 to 1 1/2 pounds green beans, trimmed
8 boiled eggs, peeled and quartered
32 black olives, Nicoise or kalamata
Whisk shallots, lemon juice, mustard, vinegar, and 1/4 teaspoon each: salt and pepper in a small bowl or 2-cup liquid measuring cup. Slowly whisk in 1 cup of the oil, first in droplets then in a steady stream to make thick vinaigrette. Coat tuna with 1/2 cup of the vinaigrette; set remaining vinaigrette aside.
Keeping potatoes, tomatoes, and green beans separate, toss each with 1 tablespoon of the remaining oil and sprinkle generously with salt and pepper. Place green beans on a large wire rack. Heat gas grill, igniting all burners on high for at least 10 minutes, or build a hot charcoal fire. Clean grate with a wire brush, then lubricate with an oil-soaked rag.
Place potatoes and tomatoes on hot grill rack. Cover and cook, turning potatoes once and not turning tomatoes at all, until potatoes are grill marked and cooked through and tomatoes are soft, about 10 minutes. Divide potatoes and tomatoes between 2 platters; set aside.
Close grill lid and return to hottest state. Place tuna and green beans on hot grill rack (green bean wire rack turned perpendicular to grill rack). Cover and cook, turning once, until tuna is grill marked on both sides and cooked to medium, 5 to 6 minutes, and until green beans are tender-crisp, turning occasionally, about 10 minutes. Arrange tuna and green beans on each platter. Arrange eggs over potatoes, tomatoes, green beans and tuna and scatter olives over each platter. Serve warm or at room temperature.