I roasted mine over a gas burner until completely charred and blackened. I set them on a dinner plate then placed another plate on top and let them steam for about 10-15 minutes. Peel the skin off then slice for the recipe. Do not rinse the chiles to remove the skin, just use your fingers. You can also use a zip top bag to steam.
For the soup:
Heat oil in a large pot over medium heat. Add sliced onions and chopped garlic and cook until softened, about 4 or 5 minutes.
Add chopped tomatoes, dried oregano, and salt and pepper. Cook until softened, about 3 minutes.
Add potatoes, mix well then add water and bouillon. Stir soup ingredients to combine. Bring soup to a simmer, then add a small bunch of fresh cilantro (I used about 5-6 long sprigs). Cover and simmer until potatoes are fork tender, about 25 to 30 minutes (depending on type of potato used).
When potatoes are tender, remove the cilantro and discard. Add sliced green chiles and milk. Warm milk first, if desired. Stir and heat through. You can add the cheese cubes at this point, or you can place them in soup bowls and pour the hot soup over.
Notes
If you are rushed for time, skip roasting the chiles and used canned or frozen.
Serve with corn chips, tostada chips, flour tortillas, pico de gallo, and chopped cilantro.
Let soup cool before storing in an air-tight container. Keep in the refrigerator for 3 or 4 days. Freeze for up to 3 months.
Thaw overnight in the refrigerator and reheat in on the stove top or microwave until hot.