I found this hatch Green Chile Colorado recipe, looks pretty tasty.
INGREDIENTS
1 tablespoon bacon drippings
1 tablespoon olive oil
4 pounds pork loin roast
1 onion chopped
5 garlic cloves peeled and minced
1 quart chicken broth
1 tablespoon salt
1½ tablespoons coriander
1 teaspoon hot Chamayo Chili Powder
1 teaspoon of your favorite chili powder
1½ tablespoons Mexican Oregano
14.5 ounces can chopped tomato, undrained
15 chile peppers chopped
1 teaspoon sweet smoked paprika
juice of ½ lime
½ cup water
¼ cup cornstarch
INSTRUCTIONS
Simply season the pork roast with salt and pepper. Place in a large Dutch oven, cover and roast in a 350 degree oven until done. About 3 hours. Remove the roast from the pan and let cool and then shred the meat with two forks. Set aside.
Heat the oil and the bacon drippings in the same Dutch oven. Add the onion and cook until soft, about 10 minutes . Add the garlic and cook until fragrant.
Add the shredded meat, tomatoes, chicken broth, salt, coriander, oregano, tomatoes, chile powders and chiles. Bring to a boil and then simmer on low for 2 hours..
In a bowl combine water and cornstarch and stir until combined. Towards the end, I like to add a little of this to thicken the soup.
Serve with warm flour tortillas.