Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper. If your puff pastry is frozen, thaw it according to package directions before using. Lightly flour your work surface.

In a mixing bowl, crumble or grate 2 cups feta. Add 2 cups ricotta and 1 large egg. Mix until evenly combined. Stir in chopped fresh dill if using.

Divide the cheese mixture into four equal portions.

Working with one puff pastry sheet at a time, gently roll it on the floured surface to smooth seams and slightly enlarge it.

Place one quarter of the cheese mixture in a log along one short edge of the pastry sheet, leaving a small border at the edges. Fold the edges over the filling and roll away from you to enclose the filling, forming a sealed roll. Repeat with the remaining sheets and filling.

Transfer each roll to the prepared baking sheet with the seam side down. Brush each roll with the beaten large egg reserved for egg wash. Sprinkle sesame seeds on top if desired. Make two small slits or prick each roll with a fork to allow steam to escape.

Bake in the preheated oven for 25–30 minutes, or until the pastries are deep golden brown.

Remove from oven and let the pies cool on the baking sheet for 5–10 minutes, then transfer to a wire rack to cool slightly before slicing and serving.