Preheat the oven to 375°F (190°C).

In a skillet, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes. Then, add the grated zucchini or pumpkin and cook for an additional 5-7 minutes until the moisture has evaporated. Remove from heat and let cool slightly.

In a mixing bowl, combine the cooled zucchini or pumpkin mixture, crumbled feta cheese, chopped herbs, and eggs. Season with salt, pepper, and nutmeg if using. Mix well to combine.

Grease a baking dish and layer half of the phyllo dough across the bottom. Brush each layer with olive oil as you go.

Pour the zucchini mixture over the phyllo layer. Top with the remaining phyllo sheets, brushing each layer with olive oil again.

Tuck the edges of the phyllo dough into the sides of the dish to seal the filling.

Bake in the preheated oven for 30-40 minutes, or until the phyllo is golden brown and crispy.

Let cool before slicing and serving. Enjoy your kolokithopita warm or at room temperature.