For the dressing: Use a mortar and pestle to grind the garlic cloves and the salt to a paste. (This dressing can also be made in the blender or food processor.) Bring a small pot of water to a boil and add the eggs. Cook for 2 1/2 minutes and remove from the water. Meanwhile, transfer the garlic to a bowl and whisk in the lemon juice, caper juice, Worcestershire, hot sauce and tuna. Peel and add the eggs and 1/2 cup olive oil and whisk until smooth. Taste for seasoning. Set aside.
For the croutons: Heat a large skillet over medium heat. When it begins to smoke lightly, add the butter. Add the bread and season with salt and paprika. Toss and cook over medium to low heat until they become brown and feel crispy to the touch, 5 to 8 minutes. Season with salt and the oregano. Drain on paper towels. Sprinkle with some of the grated Parmesan.
To serve: In a large bowl, toss the lettuces in the dressing. Toss in the croutons, basil leaves and the remaining Parmesan. Serve immediately.