Heat the olive oil in a large pot over medium heat. Add the onion and cook 3 to 4 minutes until softened. Stir in the garlic and cook 30 seconds until fragrant.
Add the shredded chicken, green enchilada sauce, and chicken broth. Bring to a simmer and cook 10 minutes.
Stir in the cooked rice and cream. Add cumin, salt, and pepper to taste. Simmer for 5 minutes more until heated through and creamy.
Taste and adjust seasoning. Serve hot with your favorite garnishes.