Heat the oil in a skillet over medium heat, and cook the onion until tender. Mix in the garlic, spinach, and carrots, and cook until the spinach liquid has evaporated. Remove skillet from heat, and mix in cheese and eggs. Season with red pepper, nutmeg, salt, and pepper. Pour 1/2 the mixture into each pie shell.
Bake 30 minutes in the preheated oven, until a toothpick inserted in the center of a quiche comes out clean.
