Add olive oil to a soup pot or Dutch oven over medium-low heat. Add diced onion and saute until translucent, about 4 to 5 minutes. Add minced garlic and cook for 1 more minute until just beginning to color.

Add oregano, cumin, salt, pepper, paprika, and cayenne pepper if using. Saute the spices for 1 full minute to bloom their flavor before adding liquid.

Pour in the chicken stock and add the can of green chiles. Stir well to combine, then raise the heat until the mixture reaches a low boil.

Reduce heat to a gentle simmer. Cook uncovered for about 25 minutes, stirring occasionally, until the stock has reduced by at least one third.

Turn heat down to medium. Add the heavy whipping cream, cream cheese cut into small cubes, and shredded rotisserie chicken. Cook for 10 to 15 minutes, stirring frequently, until the cream cheese has fully melted and the chili is heated through.

Taste and adjust seasoning with salt and pepper as needed. Remove from heat and serve topped with shredded cheese, sour cream, diced avocado, or pork rinds.