Heat the oil in a Dutch oven over medium-high heat and cook the chicken with 1 teaspoon salt for 6 to 8 minutes until it reaches 165°F; transfer it to a plate.
Cook the onion for 5 minutes, then stir in the cumin for 30 seconds.
Mash 1 cup beans and add them with the whole beans, green chiles, broth and remaining salt and bring to a boil.
Add the macaroni and cook for 2 minutes less than the package directs, adding the corn during the final 3 minutes.
Return the chicken, remove the pot from direct heat and stir in the Monterey Jack a handful at a time.