Heat olive oil in a large Dutch oven over medium-high heat.
Add diced onion and cook 4-5 minutes until softened; then add minced garlic and cook 1 minute.
Add chicken breasts and enough broth to cover; bring to a boil, then simmer 20 minutes until cooked through. Remove, shred, and set aside.
Add beans, green chiles, and spices; bring to a boil, then simmer 10 minutes. Stir in corn and cook 3 minutes.
Reduce heat to low; add cream cheese and stir until melted. Mix in heavy cream and Monterey Jack cheese until smooth. Return shredded chicken to pot and cook 2 minutes until heated through.
Notes
For extra flavor, top with fresh cilantro and sliced avocado before serving.