Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
In a mixing bowl, combine the chopped spinach, crumbled feta cheese, and softened cream cheese. Mix until well blended.
Add the all-purpose flour, olive oil, egg, garlic powder, onion powder, black pepper, salt, and dill to the spinach mixture. Stir until all ingredients are thoroughly combined.
Roll out the thawed puff pastry on a lightly floured surface to ⅛ inch thickness.
Cut the pastry into squares or circles, about 3 to 4 inches in size, using a knife or pizza cutter.
Place a generous tablespoon of the spinach filling in the center of each pastry piece.
Fold the pastry over the filling to form a triangle or half-moon shape, sealing the edges with a fork or your fingers.
Arrange the filled cookies on the prepared baking sheet. Brush the tops with olive oil for a golden finish.
Bake in the preheated oven for 20-25 minutes, or until the pastry is golden brown.
Remove from the oven and allow to cool for a few minutes before serving.