Heat olive oil in a large pot over medium heat. Add onion and jalapeño; sauté for 6–7 minutes until softened.
Stir in chicken broth, green enchilada sauce, green chilies, and cubed cream cheese. Stir until cream cheese melts into the soup.
Add shredded chicken, 1 cup of Monterey Jack cheese, and chopped cilantro. Stir and let simmer for 5–6 minutes. Add more broth if you prefer a thinner soup.
Taste and adjust seasoning with salt and pepper.
Prepare fried tortilla strips by slicing corn tortillas into thin strips and frying them in hot oil until golden and crisp. Drain on paper towels.
Ladle soup into bowls and top with fried tortilla strips, avocado, extra cheese, cilantro, and sour cream if desired.