Combine olive oil, anchovy paste and garlic in a bowl, and mash to form a paste. Transfer the paste to a heavy saucepan.
Add the remaining ingredients and stir well. Place over medium heat and bring to a simmer. Reduce the heat to low and cook, covered, stirring frequently, for 1 hour.
Allow to cool to room temperature.
Cut loaf of bread in half lengthwise, making the bottom half larger. Hollow out the halves, using your hands or a melon baller to create a shell. Discard the in side and place the tops aside.
Drizzle the olive oil over the bottom half of the bread. Layer the tomatoes and red onion over the bread, and season with pepper. Scatter the tuna over the onion, and press it down lightly. Then spread 1/3 cup of the tomato sauce over each loaf.
Slice 2 of the eggs, and arrange the slices over the tomato sauce. Slice the lettuce crosswise and cover the eggs with the lettuce. Then spread the remaining tomato sauce over the lettuce.
Grate the remaining egg over the sauce and sprinkle with the parsley. Replace the top of the loaf, and press down lightly.
To serve, cut into sandwich-size slices or slice thinly for hors d'oeuvres.