Arrange tart shells on a baking sheet. Fill each shell with about 1 tablespoon each spinach and cheese.
Whisk together eggs and next 3 ingredients. Spoon egg mixture evenly into tart shells. Sprinkle lightly with nutmeg.
Bake at 375° for 30 to 35 minutes or until tarts are puffed and crust is lightly browned. Let stand 5 minutes before removing from foil pans.
Make Ahead: To make ahead, simply fill the pastry with the spinach and cheese, and prepare the egg mixture. Cover both, and chill overnight. Next day, fill tarts with egg mixture, and bake.