If using freshly roasted green chile, remove the skin, deseed and dice. For frozen green chiles, thaw and dice if they don't come chopped, though most frozen green chiles tend to come diced. You can also used canned green chiles, though fresh or frozen is my preference.
In a large stockpot, heat olive oil over medium-high heat. Liberally salt and pepper the pork shoulder roast. Once the oil is hot, cook the pork on all sides until it develops a nice crust. This should take about four to five minutes on each side. Remove the pork, add the onion and turn heat down to medium. Cook for about five minutes. Add the garlic and cook for about 30 seconds.
Put the pork back in the stockpot and add the chiles, cumin, spiced paprika, pepper, chicken broth and potato to pot. Bring to a low boil. Reduce heat to low, cover and simmer until the pork is fork tender, about two to three hours.
When the pork is tender, remove the roast from the stockpot and shred with two forks once it's cool enough to handle. Discard any bones.
In a separate skillet, melt the butter to make a roux. Continuously whisk in the masa or flour for about four to six minutes. Return the shredded pork to the stockpot and stir in the roux. Cook for another five to 10 minutes until the green chile thickens to your liking.
Taste the green chile and if you'd like to add more heat, stir in cayenne pepper or sauteed diced fresh jalapenos with the seeds. This step is optional. You can also add more salt to taste if desired. Turn off heat and stir in lime juice.
You can serve immediately or refrigerate it overnight to allow the flavors to meld. Smother or eat as a stew. Garnish with your favorite toppings. Enjoy!