Preheat your oven to 375°F.
In a mixing bowl, combine the softened cream cheese, butter, minced garlic, parsley, sugar, salt, black pepper, and red pepper flakes (if using). Mix until well combined and creamy.
Cut each bread roll in half horizontally, without cutting all the way through, creating a pocket for the filling.
Generously spread the cream cheese mixture inside each pocket of the bread rolls.
If desired, sprinkle shredded mozzarella cheese on top of the cream cheese mixture.
Wrap each filled bread roll in aluminum foil and place them on a baking sheet.
Bake in the preheated oven for 15-20 minutes, until the bread is warm and the cheese is melted.
Remove from the oven, unwrap the foil, and serve warm.