01Preheat oven to 350 F. Line a large baking sheet with parchment paper.
02Using a serrated knife, cut the rolls into 6 equal wedges, being sure not to cut all the way through the roll. Set aside.
03In a medium bowl, using an electric mixer on medium-speed, beat together the cream cheese and sugar until fluffy and smooth. Add the heavy cream and continue to beat until smooth. Place the cream cheese mixture into a pastry bag with a large top, or a large plastic bag, and cut off a tip at an angle. Pipe a generous amount of cream cheese mixture into the slices in each of the rolls.
04In a medium bowl, whisk the melted and cooled butter, eggs, and milk until smooth. Stir in 1/4 cup of the Parmesan cheese, minced garlic, and minced parsley.
05Dunk the rolls into the garlic butter mixture, coating them completely and letting butter soak into the bread. Double dip if there is leftover mixture. Place on the prepared baking sheet.
06Sprinkle rolls with remaining 1/4 cup Parmesan cheese.
07Bake for 10 to 15 minutes, or until golden brown on top.