Heat olive oil in a large Dutch oven or heavy pot over medium heat. Add diced onion and sauté for about 5 minutes until softened and translucent.
Stir in minced garlic and cook for 1 additional minute, stirring constantly until fragrant. Do not let it burn.
Add shredded chicken, chicken broth, heavy cream, corn, black beans, and enchilada sauce to the pot. Stir well to combine all ingredients.
Season the soup with cumin, chili powder, smoked paprika, salt, and pepper. Bring the mixture to a simmer over medium heat.
Reduce heat to medium-low and let the soup cook for 15-20 minutes, stirring occasionally. The soup will thicken slightly as it simmers.
Add cubed cream cheese to the soup and stir until completely melted and incorporated, about 2-3 minutes. The soup will become smooth and creamy.
Remove from heat and stir in shredded cheese until melted and smooth. Taste and adjust seasoning with additional salt, pepper, or chili powder if needed.
Ladle hot soup into bowls and garnish with fresh cilantro, extra cheese, diced avocado, sour cream, and tortilla chips. Serve immediately.