1. Heat the oil in a large skillet over medium heat and cook the beef or pork until browned and cooked through.

2. Add the diced onion and cook until softened, then stir in the garlic and cook for 30 seconds.

3. Add the Hatch green chiles, green enchilada sauce or salsa verde, chicken broth, cumin, oregano, salt, and black pepper.

4. Simmer the mixture for 8 to 10 minutes until slightly thickened and flavorful.

5. Stir in 1 cup of the shredded cheese and half of the cilantro, then remove from the heat.

6. Warm the flour tortillas until soft and flexible.

7. Divide the filling among the tortillas and top with the remaining cheese.

8. Fold in the sides, roll each tortilla tightly into a burrito, and place seam side down.

9. Return the burritos to a lightly greased skillet and cook for 2 to 3 minutes per side until golden and crisp.

10. Serve hot with extra cilantro, green sauce, sour cream, or avocado if desired.