Rinse the quinoa and cook it in 1⅓ cups of water, chicken broth, or vegetable broth.
While that's cooking, dice the onions, mince the garlic, cut the carrots into bite-size pieces, and dice the peppers. And measure out the spices into a small dish.
When the quinoa is almost ready, heat the olive oil in a large pot over medium-high heat.
Sauté the onion until transparent.
Add the garlic and continue cooking a minute.
Add the diced tomatoes, tomato sauce, cooked quinoa, broth, green chiles, carrots, and spices.
Bring it to just a boil, then reduce the heat and simmer for 20 minutes or so.
Mix in the diced peppers and continue cooking until the carrots are the right softness, usually about 15 minutes.
Empty cans of beans into a collander and drain beans.
Rinse beans (otherwise you may need to eat this chili with a gas pill on the side!)
Mix in the beans, corn, cilantro, and lime and continue cooking long enough to warm them up.
Serve warm with toppings.