Place the eggs in a saucepan and cover them with water. Bring to a boil, then reduce the heat and simmer for approximately 9–12 minutes, depending on the desired firmness. Transfer the eggs to cold water, allow them to cool, peel, and slice.
Wash the tomatoes, cucumber, and lettuce. Slice the tomatoes and cucumber thinly, and cut the red onion into delicate rings. Drain the capers and olives. If using anchovies, drain them and cut them into small pieces.
Place the drained tuna in a bowl and gently flake it with a fork. If you are using tuna packed in water, add a little extra olive oil to improve the flavor and texture.
Whisk together the extra-virgin olive oil, red wine vinegar, Dijon mustard if using, black pepper, and a small amount of salt. Taste the dressing before adding more salt, particularly if your olives, capers, or anchovies are salty.
Slice the round bread horizontally into a top and bottom half. If the interior is very thick, gently remove a little of the soft crumb from both halves to make room for the filling. Keep enough bread intact to hold the sandwich together.
Brush or drizzle the olive oil dressing over the cut surfaces of the bread. Allow the bread to absorb some of the dressing, especially around the center. This step helps create the characteristic moist, flavorful texture of Pan Bagnat.
Arrange the tomato slices over the bottom half of the bread. Add the tuna, sliced eggs, red onion, olives, capers, basil, and optional anchovies. Add cucumber and lettuce if desired, but avoid overfilling the sandwich.
Drizzle any remaining dressing over the filling. Spread the ingredients evenly so that each portion contains a balanced combination of tuna, vegetables, eggs, and olives.
Place the top half of the bread over the filling. Wrap the sandwich tightly in food-safe parchment or plastic wrap, then place a light, flat weight on top. Refrigerate for approximately 30–60 minutes to help the flavors mingle and the bread absorb the dressing.
Unwrap the sandwich and cut it into two portions using a sharp serrated knife. Serve chilled or cool, accompanied by a green salad, fresh fruit, or vegetable crudités.