Place the chicken thighs, chicken broth, diced tomatoes, diced green chiles, heavy whipping cream, chili powder, salt, dried parsley, cumin, garlic powder, onion powder, dried oregano, and black pepper in the Instant Pot and stir well. The mixture will look loose at this stage, but the seasonings should be evenly distributed through the broth.

Arrange the cream cheese pieces around the pot, lock the lid, set the valve to seal, and cook on high pressure for 15 minutes, then let the pressure come down naturally for 10 minutes before venting the rest. When you open the lid, the chicken should be very tender and the broth should look lightly creamy rather than fully blended.

Shred the chicken directly in the pot with an electric hand mixer or two forks. The chili should start to look thicker and more uniform as the shredded chicken mixes back into the broth.

Stir in the cauliflower rice and let the chili stand for 2 minutes. The cauliflower should heat through quickly and the broth should shift from brothy to velvety.

Add the chicken broth, diced tomatoes, diced chiles, chili powder, salt, dried parsley, cumin, garlic powder, onion powder, dried oregano, and black pepper to the slow cooker and stir to combine, then add the chicken thighs and cream cheese. The cream cheese will sit in pieces at first, which is fine because it softens as the chili cooks.

Cover and cook on high for 3 to 4 hours or on low for 6 to 8 hours. By the end, the chicken should pull apart easily and the pot should smell deeply savory and warm with cumin and oregano.

Stir in the cauliflower rice 20 minutes before serving. The cauliflower should soften and absorb flavor while the broth becomes thicker and creamier.