Cut the chuck roast into 2–3 inch chunks and pat dry.
In a small bowl, whisk together chili powder, 1 teaspoon ground cumin, garlic powder, Mexican oregano, and kosher salt.
Season the beef chunks with the spice mixture and massage the spices into the meat with your hands.
Set the Instant Pot to sauté, add the avocado oil, and cook the diced onion until it begins to soften, about 3–4 minutes.
Add the remaining 1 teaspoon ground cumin to the softened onion and stir until fragrant, about 30 seconds.
Turn off sauté mode. Add the seasoned beef, beef broth, tomato paste, and either the 14-ounce can of diced tomatoes with chiles or the 3–4 (4-ounce) cans of diced green chiles to the pot.
Lock the lid and set the Instant Pot to the Meat/Stew or high-pressure setting. Cook on high pressure for 35 minutes.
Allow the pressure to release naturally when cooking completes, then carefully open the lid.
Remove the meat to a platter and shred with two forks, then return the shredded beef to the sauce and stir to combine.
Serve the shredded beef as desired.