Remove the stems from the spinach, chop the leaves coarsely and rinse well in several changes of water. Drain and set aside.
In a large frying pan over medium heat, warm the olive oil. Add the green onions and sauté until tender, about 5 minutes. Transfer to a bowl.
Add the spinach to the same pan and place over high heat. Cook, turning the spinach with tongs or a fork, until wilted, about 4 minutes. (The leaves will wilt in their own moisture.) Transfer to a sieve and drain well, pressing out the excess moisture with the back of a spoon.
Chop the spinach coarsely. Add it to the green onions, then stir in the parsley, dill and feta cheese. If the feta is salty, add the cottage cheese to mellow the overall flavor. Add the eggs and nutmeg and stir well. Season to taste with salt and pepper. Set aside.
Butter an 11x16 1/2" baking dish. Remove the filo sheets from their package, lay them flat on a work surface and cover with a damp towel or plastic wrap to prevent them from drying out.
Lay a filo sheet in the prepared dish and brush it lightly with the butter. Top with 8 more filo sheets, brushing each one with butter. Spread the spinach mixture evenly over the filo layers. Then top with the remaining 9 filo sheets, again brushing each sheet lightly with the butter, including the top sheet. Cover and refrigerate the pie for 30 minutes so the butter will set.
Meanwhile, preheat an oven to 350 °F (165 °C). Using a sharp knife, cut the pie into 16 equal pieces. Bake until golden brown, about 30 minutes. Remove from the oven and let stand for 5 minutes. Re-cut the pieces and serve hot.