Heat 1 tablespoon olive oil in a medium skillet over medium heat. Add the spinach and sauté until wilted and most of the moisture has evaporated, about 3 to 5 minutes. Set aside to cool.
In a large mixing bowl, combine the feta, sautéed spinach, egg, garlic powder, za’atar leaves, and a pinch each of salt and black pepper. Mix until well combined.
Preheat the oven to 355°F (180°C) and line a large baking sheet with parchment paper.
On a lightly floured surface, gently roll out the puff pastry to even the thickness if needed. Cut into 6 to 8 equal squares. Using a sharp knife, lightly score a 1/2-inch border around each square, without cutting all the way through.
Transfer the squares to the prepared baking sheet. Brush the borders with the beaten egg and sprinkle with sesame and nigella seeds.
Spoon about 2 tablespoons of filling into the center of each square, keeping it inside the scored borders.
Bake for 15 to 20 minutes, or until the pastry is puffed and deeply golden. Let cool slightly before serving. These are best warm or at room temperature.