You can make this recipe without mayonnaise. Simply substitute two egg yolks for the mayonnaise portion, and whisk in additional extra virgin olive oil (about ¼ cup) until the desired dressing consistency is reached.
For the croutons: I mixed 2 tablespoons of melted butter with 2 tablespoons grated Parmesan. I tossed that with 4 cups of bread chunks from a leftover loaf. I baked at 375ºF for 15 minutes, stirring once about halfway through.