Place eggs in a single layer in a 4- to 5-quart saucepan. Add enough water to cover eggs by about 1 inch. Cover pot and set over high heat; bring to a boil. Remove from heat; let stand 15 minutes. Set aside to cool. When cool, peel and slice in half lengthwise.
Meanwhile, refill pot with water and bring to a boil over high heat. Blanch beans: Boil until bright green and crisp-tender, about 7 minutes; immediately plunge beans into ice water to stop cooking. Drain and set aside.
Sprinkle salt and pepper onto fresh tuna; press them into flesh on both sides.
Pour oil into a large skillet and set over medium-high heat. Working in batches to avoid overcrowding, sear tuna on one side to create a peppery crust, about 3 minutes. Turn carefully and sear other side (interior should still be red). Remove tuna to a platter.
Let sit about 10 minutes; then slice and arrange. Add little piles of green beans, radish slices, and egg slices, and arrange. Place little piles of olives around and in between these ingredients.
In a separate salad bowl, toss lettuce with enough Simple Vinaigrette to coat. Place a pile of lettuce leaves on each individual serving plate; guests may select toppings from the large platter. Serve with Aioli.
Whisk together vinegar, salt, and pepper. Slowly drizzle in oil, whisking continuously, to form an emulsion. Yield: about ⅓ cup
This Catalan-style garlic sauce is great for summer days because it contains eggs, so it can take the heat without spoiling.
Crush garlic and salt in a mortar with pestle to a fine paste. Transfer to a nonreactive bowl. Drizzle in oil very, very slowly, whisking continuously to form an emulsion. Go as slowly as possible here, letting the garlic paste absorb the oil before adding more. The mixture should be very thick and creamy when you’re done. Yield: about ¾ cup