Preheat the oven to 350°F and line a baking sheet with parchment paper.
In a mixing bowl, beat the softened cream of cheese until creamy. Add sugar and blend well, then incorporate the heavy cream until the mixture is smooth.
Transfer the cream cheese mixture into a piping bag.
Slice the rolls into 6-8 wedges without cutting through the bottom. Pipe the cream cheese filling into the wedges.
Whisk together melted butter, egg, and milk. Stir in minced garlic and chopped parsley.
Dip the filled rolls into the garlic butter mixture, ensuring it seeps into the wedges.
Place the rolls on the prepared baking sheet, sprinkle with optional Parmesan, and bake for 5-10 minutes until golden.