Preheat your oven to 375°F (190°C) and generously grease a 12-cup muffin tin with butter or cooking spray. Place the muffin tin in the refrigerator while preparing the filling.
Lightly flour your work surface. Unwrap the thawed puff pastry sheets and let them sit at room temperature for 5 minutes.
In a medium bowl, combine the softened cream cheese, mozzarella, Parmesan, minced garlic, chives, oregano, red pepper flakes (if using), and black pepper. Mix until well incorporated but still textured.
On your floured surface, gently roll out one sheet of puff pastry to approximately 12×16 inches, maintaining an even thickness of about ⅛ inch.
Spread half of your cheese mixture evenly over the entire surface of the rolled pastry, leaving a ½-inch border around all edges. Gently press the filling into the dough.
Starting from the long edge, tightly roll the pastry into a log, sealing the edge with a light press. Using a sharp knife, cut the log into 6 equal portions.
Repeat the rolling, filling, and cutting process with the second pastry sheet and remaining filling.
Place each cut portion into your prepared muffin tin, spiral side up. Brush each cruffin with beaten egg.
Combine the Parmesan, garlic powder, and a pinch of parsley. Sprinkle this mixture over the egg-washed cruffins.
Bake in the preheated oven for 22-25 minutes, or until the cruffins are puffed and golden brown, with the cheese filling bubbling slightly.
Remove from the oven and immediately brush with melted butter. Let cool in the tin for 5 minutes, then carefully transfer to a wire rack.
Sprinkle with remaining parsley while still warm before serving.