Heat olive oil in 2-quart saucepan. Add onions and saute until tender, about 3 minutes. Add spinach and cook 1 minute. Remove pan from heat.
Stir lemon rind, parsley and feta cheese into spinach mixture. Combine cottage cheese, Romano cheese and egg in a small bowl. Stir until well blended. Add to spinach mixture. Add salt, pepper and nutmeg; stir well.
Scrape filling into a 9-inch pie plate or 8-inch square baking dish. Bake 15 minutes. Remove from oven.
Brush one sheet of fillo with melted butter, keeping remaining sheets covered with a cloth. Crumple fillo sheet into a nest shape and place on top of fillo. Repeat with remaining fillo sheets to cover filling.
Bake about 10 minutes, until fillo topping is browned.