The addition of Parmesan is of my own doing, I'm pretty sure Panera doesn't use it but I like to for a finishing touch that adds a little richness and one last layer of flavor. (cinnamonspiceandeverythingnice.com)
A little richness from the buttermilk and egg with a little bit of butter, and just a hint of sweetness from one tablespoon of brown sugar. (delectablymine.com)
You might lose a little richness, but I think it would still work. (pink-parsley.com)