Preheat oven to 375°F (190°C). Lightly oil a 9×13-inch rectangular baking dish or a 9-inch round pie plate.
If using fresh spinach, remove any tough stems and roughly chop. Blanch in boiling water for 30 seconds, then transfer to an ice bath. If using frozen spinach, thaw completely.
Place spinach in a clean kitchen towel and wring out all excess moisture. Chop finely and set aside.
Heat 2 tablespoons olive oil in a skillet over medium heat. Sauté onion until translucent, about 5 minutes. Add garlic and cook for 30 seconds more. Allow to cool.
In a large bowl, combine feta, ricotta, and Parmesan cheeses. Add the spinach, onion-garlic mixture, dill, parsley, mint, lemon zest, nutmeg, salt, and pepper. Mix well.
Create a well in the center and add the beaten eggs. Fold everything together until fully incorporated. Set aside.
Unroll phyllo dough and cover with a damp kitchen towel to prevent drying. Work with one sheet at a time, keeping the rest covered.
Place one phyllo sheet in the prepared baking dish, allowing edges to hang over. Brush lightly with melted butter. Repeat with 8-10 sheets, brushing each with butter.
Spread the spinach filling evenly over the phyllo base.
Fold any overhanging phyllo edges over the filling. Top with 8-10 more phyllo sheets, brushing each with butter.
Tuck edges down sides of dish and brush the top generously with butter.
Score the top crust into serving portions with a sharp knife, cutting through just the top few layers.
Bake for 45-50 minutes, or until the top is golden brown and the filling is set.
Remove from oven and let rest for 15-20 minutes before serving.
Cut along pre-scored lines and serve warm or at room temperature.