Thaw the frozen spinach and squeeze it thoroughly (Note 5).
Puff pastry: If using frozen puff pastry, thaw and roll it according to the package instructions. If using refrigerated and already rolled pastry, remove it from the fridge about 10 minutes before baking.
Preheat the oven to 375°F/ 190°C. Brush the baking dish with olive oil.
Beat the egg in a cup. Remove about ¼ of the egg and keep it separated for later; you will need it to brush the pastry before baking.
Filling: Place squeezed spinach in a medium bowl. Add the egg (except for what you saved for brushing) finely chopped onions, grated garlic, crumbled feta, dried mint, chopped dill, lemon zest and juice, salt, and black pepper. Combine well and adjust the taste if necessary.
Drape the dough sheet over the baking dish.
Spread the feta and spinach filling inside the pastry, then fold in the corners and sides of the dough toward the center. The filling will not be fully covered in the middle. Trim a bit of the dough corners and sides to make the pie look nice.
Egg wash: Mix the beaten egg you’ve saved with the milk and brush the pastry with the mixture. Sprinkle it with sesame seeds.
Bake in the preheated oven for 20-25 minutes until the pastry is puffed up and deeply golden.
Let sit for about 5 minutes before slicing.