Pat the pork cubes dry with paper towels and season with salt and pepper. Heat the oil in a large Dutch oven or heavy-bottomed pot over medium-high heat.
Working in batches to avoid crowding the pot, sear the pork on all sides until well browned, about 5 to 7 minutes per batch. Transfer the browned pork to a plate and set aside.
Reduce the heat to medium. Add the chopped onion to the pot and cook, stirring occasionally, until softened, about 5 minutes. Add the minced garlic and ground cumin, and cook for 1 minute more until fragrant.
If using, sprinkle the flour over the onions and stir constantly for 1 minute to cook off the raw taste. This will help thicken the final sauce.
Stir in the chopped roasted green chiles and cook for 2 minutes, scraping up any browned bits from the bottom of the pot. Return the seared pork and any accumulated juices to the pot.
Pour in the chicken broth and add the oregano. Stir everything together well.
Bring the mixture to a boil, then reduce the heat to low. Cover the pot and let it simmer gently for 2 to 2.5 hours, or until the pork is fork-tender. Check the pork for doneness; it should shred easily.
Once the pork is tender, check the seasoning and add more salt if needed. The internal temperature of the pork should be at least 145°F (63°C). If the sauce is too thin, remove the lid and simmer for another 10 to 15 minutes to reduce.
Serve the chili verde warm in bowls, accompanied by flour tortillas.