For the dressing, combine the clove of grated garlic and the smoked sardines in a small bowl and mash to a rough paste with a fork. Add the mayonnaise, 1/2 cup of the Parmesan cheese, the lemon juice, 3 tablespoons of the olive oil, 1/4 teaspoon salt and 1/2 teaspoon pepper, and mix together. Thin the dressing with a tablespoon or so of water, until it has the consistency of thick cream.
For the croutons, heat a large heavy skillet over medium heat. Add the remaining 2 tablespoons olive oil to coat the bottom of the pan, and then add the smashed garlic cloves, butter, paprika and bread. Season with salt and pepper and cook, stirring often, until the bread turns crisp throughout and darkens on the edges, about 5 minutes. Discard the garlic, and allow the croutons to cool.
To serve, place the lettuce in a bowl and season with a little salt and pepper. Add enough dressing to coat, and then add the salumi, remaining 1 cup Parmesan cheese, the croutons and mint, and toss.
Recipe courtesy of Amy Thielen, reprinted from The New Midwestern Table. Copyright 2013 by Amy Thielen. Photographs 2013 by Jennifer May. Published by Clarkson Potter, a division of Random House LLC.