The timing of this soup will depend a lot on the age of your dried beans and hominy; you can either start early and remain flexible, or if you are concerned, split it into 2 days and make the beans and hominy the first day. Also, as written this makes a lot. Split in half if desired.
Soak the dried beans and dried hominy overnight in cold water.
The next morning, bring the the beans and hominy to a boil, covered by at least 2 inches of water.
While the water is coming to a boil, chop the onion and add it to the pot. Then add the New Mexico chile powder and the garlic.
Let the beans and hominy cook at a rolling boil for 5 minutes, then cover and reduce the heat to maintain a gentle simmer.
How long this will take depends a lot on the age of your beans and hominy; plan for at least 3 hours for them to cook. Make sure the beans and hominy remain covered by water by 2 inches.
When the beans are mostly tender and the hominy is mostly chewy-tender, add the salt and the stock base (chicken or vegetarian). Let it keep cooking if it is close to serving time; if not, turn off the heat and let it rest until 1 hour before serving.
In a large nonstick skillet, heat the oil over medium high heat. When it is hot, add the chopped yellow onion and half of the diced red onion with a pinch of salt.
Place the remaining diced red onion in a small-medium bowl and cover with cold water. Set aside.
Cook the onion until translucent, and then add the garlic, carrots and bell pepper. Add another pinch of salt.
If the beans and hominy are no longer simmering, now is a good time to bring them back to a simmer.
Cook for 5-10 minutes, until the veggies are softened and the onion is browning.
Add the spices (New Mexico chile powder, chipotle or smoked paprika, cumin). Stir. Then add the Mexican oregano by crumbling it in your fingers into the pot. Stir again.
Let the spices roast for 1-2 minutes, stirring to prevent scorching.
Add the fire roasted tomatoes. Bring to a boil and then reduce heat to simmer for 10 minutes, stirring occasionally.
Add the tomato-vegetable mixture to the beans and hominy. Stir and continue simmering, covered, for 20 minutes to blend flavor.
Add the lime juice and taste for salt. Remember some of the garnishes will add saltiness too.
Serve hot with garnishes.