Char the Hatch green chiles over an open flame or under the broiler turning often until the skin is blistered.
Remove from heat and cover them with a dish towel or place them in a plastic bag to steam for about 20 minutes. This will make it easy to remove the skins.
Dice the peppers and set aside.
Season the cubed pork with salt and black pepper.
Drizzle vegetable oil in the bottom of a large pot or Dutch oven. Bring the temperature up until the oil starts to shimmer. Add half of the pork in a single layer and leave it alone.
Resist the urge to move it around. We want to create a nice sear on each side of the meat. Once golden brown, flip the pieces over.
If the pieces don't release easily when you try to flip them, leave them alone until they do. Brown on the other side and then remove to a plate and repeat the process with the rest of the pork, adding a little more oil if needed.
Once all of the pork has browned, add it back to the pot along with any accumulated juices.
Add the chopped onion and garlic and saute until the onions are soft and slightly translucent.
Add 6 cups of chicken broth, oregano, and cumin. Season with salt and black pepper to taste.
Bring to a simmer and let simmer for 1 hour.
Add the diced chiles and tomatoes and simmer for an additional 30 minutes.
Add the diced potatoes and simmer until the potatoes are fork tender.
Mix the softened butter with the flour. Add to the stew and stir until it's fully incorporated and the broth has thickened as much as you'd like.
Serve with lime wedges and cilantro.