First Step: Roast the Chiles
Preheat your oven’s broiler. Place 12 to 15 Hatch chiles on a baking sheet and broil, turning frequently, until skins are evenly darkened and blistered but not burnt. Remove from oven, cover immediately with a dishcloth, and let them steam for 10 minutes to loosen skins.

Second Step: Brown the Pork and Aromatics
While chiles are resting, season pork cubes generously with salt and pepper. Heat 2 tablespoons of vegetable or olive oil in a large pot or Dutch oven over medium heat. Add pork, browning evenly on all sides, about 5-7 minutes. Add the finely chopped onion and minced garlic, sautéing until fragrant and softened. If using Anaheim chiles, add diced jalapenos here for extra heat.

Third Step: Add Liquids and Spices
Pour in 6 cups of chicken or beef broth and optionally, 6 ounces of beer to deepen the flavor. Stir in ground cumin, Mexican oregano, bay leaves, black pepper, and salt. Bring the stew to a simmer, cover, and cook on low heat for about an hour, letting the pork tenderize and flavors meld.

Fourth Step: Prepare and Incorporate Chiles
Peel the skins off the roasted Hatch chiles and finely chop them, including seeds for more heat if preferred. Add the chopped Hatch chiles and the canned diced green chilies to the pot. Simmer uncovered for 30 additional minutes to blend flavors.

Fifth Step: Add Potatoes and Simmer
Add diced potatoes to the stew. If the stew appears too thick, add up to 1 cup of hot water or broth to maintain a comfortable consistency. Continue simmering for another 15 to 20 minutes until potatoes are tender but not mushy.

Final Step: Thicken the Stew and Serve
In a small skillet, melt butter and whisk in flour, cooking for about 2 minutes to create a roux. Gradually whisk this roux into the simmering stew, stirring constantly to prevent lumps. Cook for a few more minutes until the stew thickens to your liking. Alternatively, use cornstarch mixed with water for gluten-free thickening. Adjust salt and pepper before serving.