In a Dutch oven, add the olive oil, onions, jalapenos, and garlic and cook for 2 or 3 minutes or until the onions are wilted and soft, stirring so they do not scorch.
Add the green chiles, chili powder, cumin, oregano, cayenne pepper, salt, hot sauce, enchilada sauce, and chicken stock. Stir and simmer for 20 minutes. Put a lid over the pan, propping it so the steam can escape. Stir occasionally.
If you have not already done so, remove the white and dark meat from the rotisserie chicken and chop. Set aside.
Remove the Dutch oven from the heat. Wait 10-15 minutes for the soup to cool.
Place the cream cheese into a medium-sized bowl. Add a few tablespoons of hot soup and stir. Continue doing this until the cream cheese is smooth and has liquified enough to pour. Once the soup has cooled for 10-15 minutes, slowly pour the cream cheese into the soup, whisking constantly. Alternatively, you can use an immersion blender (or regular blender) to puree the cream cheese and soup mixture to smooth all lumps.
Stir in the cream and cheese. Stir until melted.
Stir in the chopped chicken. Ladle the soup into bowls and garnish with pepper cheese and green onions.