Drizzle oil into the insert and press the Sauté button.
Once the oil is hot and shimmering (you might need to pick up the insert a bit to swirl the oil around), add the onion and salt. Stir occasionally until the onion is soft, about 5 minutes.
Meanwhile, rip off and reserve all the cauliflower leaves that look good enough to eat (a little browning is fine but they shouldn't be too dirty or shriveled). Halve the cauliflower and set one half aside for another use. Slice out and discard the core of the remaining half and chop into small florets.
Once the onion is soft, add the garlic and spices and stir for about 1 minute. Pour in 1 cup of broth and use a spatula to scrape up all the tasty brown bits on the bottom of the insert. Press the Keep Warm/Cancel button.
Toss in the cauliflower florets and add the chicken directly on top. Pour in the remaining broth (the chicken will not be fully submerged).
Secure the lid, making sure it's sealed, and press the Manual button. Set to 10 minutes. Meanwhile, rinse and thinly slice the cauliflower leaves crosswise.
As soon as the time is done, press the Keep Warm/Cancel button and release the pressure. Once it's finished de-pressurizing, remove the lid and use tongs to transfer the chicken to a bowl.
Add 1 tsp. salt and puree the vegetables and broth in the insert with a stick blender. I blend it until it's totally smooth but you can also quickly blend it so it's still a little chunky. Taste to see if it has enough salt. Add the sliced cauliflower leaves and both cans of green chiles to the broth.
When the chicken is cool enough to handle, remove the skin and tear the meat away from the bone. Add the meat to the broth, ripping it into small, bite-sized pieces. Taste one more time and adjust seasoning as necessary
Scoop into bowls and toss on your choice of toppings.