Heat the vegetable oil in a large stockpot or Dutch oven over medium-high heat.

Season the pork shoulder cubes with salt and pepper, then brown them in the pot in batches. Remove the pork and set aside.

In the same pot, add the diced onion and garlic. Sauté until softened, about 3-4 minutes.

Add the roasted Hatch green chilies, diced tomatoes, cumin, oregano, and smoked paprika. Stir well to combine.

Return the browned pork to the pot, then pour in the chicken broth. Bring the mixture to a simmer.

Reduce the heat to low, cover, and cook for 1 hour, stirring occasionally, until the pork is tender and the flavors have melded.

In a small bowl, mix the flour and water to create a slurry. Slowly stir this mixture into the chili to thicken it slightly. Cook for another 10 minutes, uncovered, to allow the chili to thicken.

Adjust seasoning with additional salt and pepper, if needed.

Serve hot, garnished with chopped cilantro and optional sour cream.