Heat the oil over medium heat in a large saucepan or soup pot.
Add the onions, garlic, cumin, achiote, oregano, salt and pepper. Mix well and cook until the onions are soft, about 5-8 minutes.
Add the chopped potatoes; mix them in until coated with onions and spices. Continue to cook them for about 5 minutes, stirring occasionally.
Add the water or broth, bring to a boil.
Add the uncooked quinoa, reduce the temperature and cook on low-medium heat until the quinoa and potatoes are tender, about 25-30 minutes. Stir occasionally. For a creamier and thicker consistency you can use a a masher or wooden spoon to crush/mash some of the potatoes.
Add the milk and cheese, stir and cook for another 5 minutes. If the soup consistency is too thick you can add additional milk to get it to your preferred texture.
Remove from the heat. Add the chopped cilantro or parsley, taste and add additional salt/pepper if needed.
Serve the quinoa and cheese soup with diced or sliced avocado and hot sauce to taste.
Notes
This soup will thicken from one day to another. If it's too thick, you can re-heat it and add addition milk or water or broth. Adjust the salt/pepper accordingly.