Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Divide your pita dough into 6 equal portions. On a lightly floured surface, roll each portion into a 6-inch / 15cm disk.
In a medium bowl, combine the crumbled feta, room temperature butter, eggs, and most of the fresh dill (reserve about 2 tablespoons / 30 ml / 1 fl oz for garnish).
Season generously with freshly ground black pepper and stir until well combined.
Spoon an equal portion of the filling onto the center of each dough disk.
Fold two opposite sides up and pinch the ends together to create an open, boat-like shape, leaving the filling exposed in the middle.
Carefully transfer the stuffed pitas to the prepared baking sheet.
Bake for 10-12 minutes, or until the dough is golden brown and the filling is set and bubbly.
Remove from the oven and sprinkle with the remaining fresh dill and optional toasted sesame seeds.
Serve warm or at room temperature.