In a large skillet, heat a tablespoon of olive oil over medium heat. Add the chopped onion and garlic, and sauté until translucent.
Add the spinach to the skillet and cook until wilted. Season with salt and pepper to taste. Remove from heat and let cool.
In a large bowl, mix the cooled spinach mixture with feta cheese, mozzarella cheese, and parsley.
Preheat the oven to 375°F (190°C). Lightly grease a baking dish.
Layer one sheet of phyllo dough in the baking dish, and brush with the egg-milk mixture. Repeat this for half the phyllo sheets.
Spread the spinach mixture evenly over the layered phyllo sheets.
Layer the remaining phyllo sheets, brushing each with the egg-milk mixture. Pour any leftover mixture over the top, and sprinkle sesame and nigella seeds.
Bake in the preheated oven for 30–35 minutes, or until golden brown. Let cool for 5–10 minutes before slicing.
Notes
Keep phyllo dough covered with a damp towel while assembling to prevent it from drying out.