Heat olive oil in a large Dutch oven over medium heat. Add diced onion and cook for 5 to 6 minutes until softened. Add minced garlic and cook 60 seconds, stirring constantly.
Add cumin, garlic powder, oregano, chili powder, coriander, and cayenne to the pot. Stir and toast in the oil for 60 seconds. Add both cans of green chiles including their liquid and stir to combine.
Nestle the raw chicken thighs into the pot. Pour in the chicken broth, enough to just cover the chicken. Bring to a gentle simmer over medium-high heat, then reduce to medium-low.
Partially cover the pot and simmer for 20 to 25 minutes until the chicken reaches an internal temperature of 74°C (165°F). Remove chicken to a cutting board.
Shred the cooked chicken with two forks into rough, uneven pieces. Return shredded chicken to the pot.
Add drained beans and stir to combine. Mash about a quarter of the beans against the pot wall with a spoon to thicken the broth. Bring back to a gentle simmer.
Reduce heat to low. Add cubed softened cream cheese and stir for 2 to 3 minutes until fully melted. Add heavy cream and stir until the broth is creamy and uniform. Simmer gently for 5 minutes.
Squeeze in fresh lime juice. Taste and adjust salt, pepper, and spices. Turn off heat and rest 5 minutes before serving with desired toppings.