To prepare the Roasted Garlic Puree:

Preheat the oven to 325 degrees F. Line a baking sheet with parchment paper or aluminum foil.

Cut the top quarter off each garlic head so the cloves are exposed. Place cut side up on the prepared baking sheet. Drizzle the oil over the garlic and season lightly with the salt and pepper. Turn the garlic cut side down. Roast until the cloves are soft and golden brown, 1 to 1 hour and 15 minutes.

Let the garlic cool. Squeeze the soft garlic flesh from each head into a bowl. Mash the flesh with a fork to blend it into a puree. (The puree can be stored in an airtight container in the refrigerator for up to 2 weeks.) Reserve 1/4 cup of the puree for the croutons and 1/4 cup of the puree to make the dressing.

To prepare the Croutons:

Increase the oven temperature to 400 degrees F.

Spread the slices of bread on a large baking sheet. Brush both sides of the slices with the olive oil, then season with the salt and pepper. Bake until lightly golden brown, 10 to 12 minutes. Cool slightly. Spread the croutons with 1/4 cup of the reserved roasted garlic puree. Set aside.

To prepare the Dressing:

Mix the mayonnaise, remaining 1/4 cup of garlic puree, cheese, buttermilk, and lemon juice in a medium bowl with a rubber spatula. Season the dressing with salt and pepper. (The dressing will keep in an airtight container in the refrigerator for 24 hours.)

Tear the larger leaves of the lettuce into bite size pieces, and leave the smaller, tender leaves whole. Toss in a large salad bowl with the sliced onions and desired amount of dressing. Adjust the seasonings with salt and pepper, to taste. Divide the greens among 4 salad plates and arrange 4 croutons on the side of each salad. Garnish the tops of each salad with 1 tablespoon of shredded Parmesan