Turn on your oven’s broiler. Place the chilies on a rack on a baking sheet.
Broil for 6-7 minutes a side until the chilies are charred. Peel off the skin, chop, and set aside.
Heat up the oil in a stock pot over medium high heat. Add in the pork. Season with salt. Brown for 10 minutes. Remove from the pot.
Add in the onion. Sauté for 5 minutes. Add in the garlic and cook for another minute.
Add the pork back in along with the chilies, potato, and seasonings.
Pour in the stock. Bring to a boil. Cover. Reduce heat to medium low and simmer for 3 hours.
In another pan, whisk together the masa flour and butter over medium heat until a roux forms. Cook for 5 minutes.
Whisk the roux into the pork green chili. Squeeze in the lime juice. Cook for 10 more minutes.