In a very large bowl whisk together the olive oil and garlic. Let sit for half an hour.
While the oil is sitting, make the croutons. Preheat the grill to medium-high. Spread the baguette slices out over a baking sheet lined with parchment paper.
Brush with olive oil (or melted butter), then grilll for a couple of minutes until the tops are lightly browned. Remove and let cool.
Add the anchovies and eggs to the oil and garlic mixture, then whisk until creamy. Add salt and pepper to taste and the lemon juice.
Whisk together with the grated Parmigiano Reggiano and adjust the seasoning or lemon juice to taste (the lemon should give an edge to the dressing, but not overwhelm it.)
Using your hands, tear off chunks of lettuce, then add to the oil mixture and toss until coated.
Coarsely chop the toasted bread and add to the salad, then top with the chopped Parmigiano Reggiano.
*All information included in this recipe has been provided by Italia Formaggi.