Lightly grease a shallow 2-quart baking dish.
Bring 3 cups water to boil in a large nonstick skillet. Add zucchini, cover, reduce heat and simmer 10 minutes or until crisp-tender. Remove to paper towels to drain.
Filling: Wipe skillet. Add lamb, onion and garlic. Cook, breaking up meat with a wooden spoon, until no longer pink. Stir in cinnamon, oregano and salt, then remaining filling ingredients. Cover and simmer 10 minutes, stirring 2 or 3 times as spinach thaws. Stir in tomato sauce. Remove from heat.
Topping: Melt butter in a 2-quart saucepan. Whisk in flour and cook, stirring 1 to 2 minutes without letting mixture brown. Gradually whisk in milk. Cook, whisking constantly, 4 to 5 minutes until thickened and smooth. Whisk about 1/3 the hot mixture into beaten eggs, then whisk egg mixture into remaining sauce. Remove from heat; stir in nutmeg.
Heat oven to 350°F.
To assemble: Cover bottom of prepared baking dish with half the zucchini slices. Spoon on all the Filling, then cover with remaining zucchini. Pour on Topping and sprinkle with cheese.
Bake 20 to 25 minutes or until hot and bubbly and top is lightly golden.