Pan Bagnat (Niçoise Salad Sandwich)

Fill a medium saucepan halfway with water; bring to a boil over high. Carefully lower eggs into boiling water; cook, undisturbed, 8 minutes. Pour off water, reserving eggs in saucepan; add ice water to cover eggs. Let eggs cool completely, about 10 minutes. Drain and peel eggs. Cut each egg lengthwise into 3 slices. Set aside.

Combine tuna, vinegar, oil, anchovies, garlic, 3/4 teaspoon salt, and 1/4 teaspoon pepper in a food processor; process just until smooth, 20 to 30 seconds, stopping to scrape down sides using a spatula as needed. Spread tuna mixture evenly onto cut sides of ciabatta halves. Scatter olives on bottom ciabatta half. Top with sliced eggs, tomatoes, onion, and radishes; sprinkle with remaining 1/4 teaspoon salt and remaining 1/4 teaspoon pepper. Top with lettuce and basil. Cover with top ciabatta half. Cover sandwich with aluminum foil or plastic wrap. Place a baking sheet on top of sandwich, and place a skillet on top of baking sheet to weigh it down. Let sandwich stand 10 to 20 minutes. Cut crosswise into 4 sandwiches, and serve.