Combine the flour, 1/2 teaspoon of the salt, and 1/4 teaspoon of the cayenne in a medium-size mixing bowl. Cut in the shortening with a pastry blender or two knives until the mixture resembles coarse meal. Add 4 tablespoons of the ice water and mix until the dough come away from the sides of the bowl, adding the remaining tablespoon of water, if necessary. Form into a ball, cover with plastic wrap, and refrigerate for at least 1 hour.

Preheat the oven to 350°F.

Remove the dough from the refrigerator and let sit for 5 minutes. Lightly dust a work surface with flour. Roll the dough out into a 12-inch round about 1/4 inch thick. Fold the dough into fourths, place it in a 10-inch quiche pan, and unfold it. Press the dough into the bottom and up the sides of the pan. Roll a rolling pin over the pan to cut off the excess dough. Prick the bottom of the crust all over with a fork.

In a large mixing bowl, combine the cream, eggs, 1/2 teaspoon of the salt, the remaining 1/8 teaspoon cayenne, and the nutmeg. Whisk to blend.

In a large skillet over medium heat, melt the butter. Add the onion, the remaining 1/4 teaspoon salt, and the black pepper and cook, stirring, until the onion is soft, about 3 minutes. Add the garlic and spinach and cook until the spinach wilts, about 2 minutes. Remove from the heat and set aside.

Arrange the spinach mixture evenly over the bottom of the crust. Sprinkle the cheeses evenly over the spinach. Pour the cream mixture over the top.

Bake until the center is set and the top is golden, about 45 minutes. Serve warm or at room temperature.