Place the eggs in a saucepan, cover with cold water by 1 inch, and bring to a boil over medium-high heat. Cover, remove from heat, and let stand 10–12 minutes. Drain, cool under cold water, peel, and slice into rounds.
Core and slice the tomatoes. Thinly slice the red onion, green bell pepper, and cucumber. In a bowl, season the tomato slices with 0.5 tsp kosher salt and 0.25 tsp black pepper; let stand 5–10 minutes until they release some juice.
Drain and flake the oil-packed tuna. Pat the anchovy fillets dry. Pit and halve the Niçoise olives if not already done. Tear the basil leaves.
Split the round country bread (boule) horizontally and, if needed, pull out a little crumb to make room. Rub the cut sides with the halved garlic clove. Drizzle 4 tbsp of the extra-virgin olive oil evenly over both cut sides and let it soak for 5 minutes; reserve the remaining 2 tbsp for finishing.
Spoon the collected tomato juices onto the bottom half of the bread, then layer the tomatoes, red onion, green bell pepper, cucumber, tuna, anchovy fillets, egg slices, and Niçoise olives. Scatter the basil leaves over the top. Drizzle with the reserved olive oil and sprinkle with the remaining salt and pepper.
Close the sandwich, press firmly, and wrap tightly in parchment or plastic. Weight with a skillet or heavy plate and rest 30–60 minutes until the bread is well saturated but still holds its shape. Cut into 4 wedges and serve.