Dice the yellow onion into ¼-inch pieces and mince the garlic cloves.
Heat the olive oil in a large pot over medium heat. Add the diced onion and cook for 5-7 minutes, stirring occasionally, until softened and translucent. Add the minced garlic and cook for another 1-2 minutes until fragrant.
Pour in the chicken broth and bring to a boil, then reduce heat to a gentle simmer. Add the green chiles, cumin, oregano, cayenne pepper, sea salt, and black pepper. Stir well to combine all the spices evenly. Simmer for 40 minutes.
Reduce the heat to low and cut the softened cream cheese into small chunks for faster melting. Stir the cream cheese into the simmering broth until completely melted and smooth. Add the heavy cream and Mexican blend cheese, stirring constantly until the cheese is fully melted.
Stir in the shredded chicken and simmer for 5 minutes to warm through and allow the chicken to absorb the flavors of the broth. Taste and adjust seasonings as needed.
