Cut the cream cheese into small pieces and set it aside to soften at room temperature.
Heat the oil and unsalted butter in a large pot over medium heat until the butter is melted. Add the onion, celery, and bell pepper. Sauté, stirring frequently, until the onions and peppers are softened.
Add the jalapeños (if using), garlic, cumin, chili powder, and oregano. Sauté for 1 minute or until fragrant.
Stir in the enchilada sauce, canned tomatoes, black beans, corn, chicken broth, and salt. Increase the heat to medium-high, bring the soup to a boil, then reduce to medium and simmer uncovered for 15 minutes.
Stir in the softened cream cheese, chicken, cheddar, and Monterey Jack cheese. Return the soup to a light simmer and cook, stirring well, for 2-3 minutes until the cheese is melted and the broth is smooth.
Season the soup to taste with salt and hot sauce if desired. Enjoy hot, garnished with chopped cilantro, sour cream, tortilla chips and/or additional cheddar or Monterey Jack cheese.