In a large sauce pan, bring about 3 quarts of water to a boil.
Add the orzo, chopped onions, and olive oil. Boil for 10 minutes, then add the zucchini and carrot coins and boil for another 5 minutes.
Drain the water out of the pan. Add the Daiya cheese, non-dairy milk, and spices, and cook over medium low heat. Stir constantly for a few minutes until the cheese melts. If the sauce seems too thick, feel free to add a little more non-dairy milk.
Add the spinach leaves, and stir them into the pasta mixture until they wilt.