Place eggs in a single layer in a non-aluminum saucepan (while fresh eggs are delicious, they are more difficult to peel; instead, use eggs that have been stored at least 10 days). Add enough water to cover 1 inch above the eggs. Cover; bring to a boil. Remove from heat; let stand 15 minutes. Set aside to cool.
Blanch the green beans by boiling them about 7 minutes, until bright green and crisp-tender. Immediately plunge beans into ice water to stop the cooking. Drain and set aside.
Sprinkle pepper and salt onto fresh tuna; press it into the flesh on both sides. Pour olive oil into a saute pan over medium-high heat. Place tuna carefully into hot pan and sear well, creating a peppery crust, about 3 minutes. Turn carefully; do the same on the other side. Remove tuna to a platter. After about 10 minutes, slice and arrange it on your platter.
On a large platter (or two), arrange the tuna, little piles of green beans, thinly sliced radishes, and the eggs, peeled and sliced in half. Put little piles of olives around and in between these ingredients.
In a separate salad bowl, toss lettuce with enough vinaigrette to coat. Place a pile of lettuce leaves on each individual serving plate; guests can select toppings from the large platter. Serve with Aioli and Romesco Sauce.
Combine vinegar, salt, and pepper. Stir to dissolve salt. Slowly drizzle in olive oil, whisking constantly, to form an emulsion. Yield: about ⅓ cup