Preheat oven to 400 degrees F (200 degrees C). Line a cookie sheet with foil.
In a large bowl, whisk together mayonnaise and milk until smooth. Whisk in eggs. Layer spinach, cheese, and onion in pie shell, making several layers of each. Pour in egg mixture. Place quiche on prepared cookie sheet. Cover quiche with foil.
Bake in preheated oven for 45 minutes. Remove cover, and bake 10 to 15 minutes, or until top is golden brown and filling is set.