Cut the feta cheese into small pieces. Chop the parsley and onion finely. Rinse and trim the spinach, shake dry and blanch in boiling salted water for 2-3 minutes. Drain, rinse with cold water and let cool. Squeeze excess water from the spinach and chop coarsley. Mix the chopped spinach with cheese, onion, nutmeg and parsley and season with salt and pepper.
Melt butter, but do not brown. Whisk the egg in a bowl and mix in the milk. Now stir in the lukewarm butter.
Grease a rectangular ovenproof dish (about 18 x 30 cm) (approximately 7 x 12 inches) with some oil. To prepare the casserole, layer half of the filo dough sheets into the baking dish. Brush each sheet with the egg and milk mixture. Spread the spinach over the sheets and cover with the remaining filo dough sheets. Brush each sheet of the cover with egg and milk mixture.
Cut the casserole in the baking dish with a knife in serving pieces and pour the remaining egg and milk mixture over. Bake in a cold oven at 200°C (fan: 180°C, gas mark 3) (approximately 400°F) for about 40 minutes. Serve warm or cold.