Set a large stock pot (at least 5 quarts) over medium-high heat and add olive oil. When oil is hot, add onion and cook until translucent, 6 minutes.
Add the potatoes and salt. Cook until the edges of the potatoes are beginning to soften and turn a golden brown, about another 5 minutes.
Add the green chiles, garlic, oregano, and crushed red pepper flakes. Cook until the garlic is fragrant, about 30 seconds, then add the stock to the pan and bring to a boil.
Reduce heat to medium-low and simmer the soup until the potatoes are tender, 10 to 15 minutes.
Add the corn kernels, peas, cheese, milk and shredded chicken to the soup. Stir and bring back to a simmer for another 5 minutes. Taste and season with black pepper and additional salt, as needed.
Notes
If you can't find canned Hatch green chiles other substitutes can be any mild green chile: Green Bell Peppers, Anaheim Peppers, Poblano Peppers.
Using fresh sweet corn adds corn milk to the broth for a nuanced flavor. 3 cups frozen corn can be substituted if fresh is unavailable though.
Mexican Cotija cheese is a moister, fattier, and less salty version of feta. Queso fresco is a good substitute, if needed.