Dice the yellow onion and mince the garlic cloves; having prepped ingredients ready helps prevent overcooking.
Heat olive oil in a large pot over medium heat; sauté onion for 5-7 minutes until translucent.
Add minced garlic and cook 1-2 minutes until fragrant.
Pour in chicken broth and bring to a boil, then reduce to a simmer.
Add green chiles, cumin, oregano, cayenne pepper, sea salt, and black pepper; stir well.
Simmer the mixture for 40 minutes to develop flavors.
Cut cream cheese into small chunks and stir into the hot broth until melted and smooth.
Add heavy cream and Mexican blend cheese slowly, stirring until fully melted and creamy.
Stir in shredded chicken and simmer for 5 minutes to warm through and meld flavors.
Taste and adjust seasoning as desired, then serve hot.