Preheat oven to 350°F. Bake pie shell, lined with foil, and pie weights or dried beans, until edges are golden, 12-15 minutes. Set aside.
Cook onion in oil over medium heat until soft, 2-3 minutes. Stir in spinach and cook until warmed through, 2-3 minutes. Transfer mixture to prepared pie shell and cover with cheese.
In a medium bowl, whisk together eggs, Chobani, milk, salt, pepper and nutmeg. Pour over pie filling and bake until quiche is just set, 35-45 minutes. Cool 15 minutes before serving.