Preheat oven to 375°F (190°C). Grease a 9x13 inch baking dish.

Heat olive oil in a large pan over medium heat. Add onion and sauté until softened, about 5 minutes.

Add chopped spinach to the pan, cook until wilted and all liquid has evaporated. Remove from heat and let cool slightly, squeezing out any excess water.

In a large bowl, combine cooled spinach, crumbled feta cheese, beaten egg, chopped parsley, black pepper, and salt (if needed, remember feta is salty). Mix well.

Lay one sheet of phyllo dough in the prepared baking dish, brush lightly with melted butter. Repeat with 4-5 more sheets, buttering each one, to form the bottom layer.

Spread half of the spinach and feta filling evenly over the phyllo layers.

Place another 4-5 phyllo sheets on top, buttering each sheet.

Spread the remaining half of the filling evenly over the phyllo layers.

Top with the remaining phyllo sheets, buttering each one. For the very top layer, ensure it's generously buttered to achieve a golden, crispy crust.

Using a sharp knife, gently score the top layers of phyllo into squares or diamonds, without cutting all the way through to the bottom. This helps with even baking and serving.

Sprinkle sesame seeds generously over the top.

Bake for 35-45 minutes, or until golden brown and crispy. If the top browns too quickly, you can lightly tent it with foil.

Let cool for 10 minutes before cutting along the scored lines and serving.