Preheat the Oven: Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper for easy cleanup.
Prepare the Filling: In a large mixing bowl, combine cream cheese, minced garlic, crumbled feta, grated pressed cheese, and chopped parsley. Mix until smooth and well combined.
Roll the Pastry: On a lightly floured surface, roll out the puff pastry into a large rectangle. Slice the pastry into strips (about 2 inches wide).
Fill and Roll: Place a generous amount of the cheese mixture onto each pastry strip. Roll them up tightly, sealing the edges to secure the filling.
Brush with Egg: Brush the tops of each roll with the beaten egg for a glossy, golden finish when baked.
Top with Cheese: Sprinkle the grated pressed cheese over the rolls before baking for an extra cheesy crust.
Bake: Arrange the rolls on the prepared baking sheet and bake for 15-20 minutes or until golden brown and puffed up.
Cool and Serve: Allow the rolls to cool slightly before serving. They are best enjoyed warm and fresh out of the oven!