First, prepare the green sauce. Puree 1 cup of the chicken broth with about ? of the tomatillos, all of the garlic, green onions and cilantro. Set aside.
Coat a large, heavy pot with oil or other fat and place on medium-high heat. Put in half the pork and season with salt and pepper, stirring until all sides are browned, about 4 minutes. Remove the browned pork, season and brown the other half and then remove all pork from the pot.
Leave any fat in the pot and cook the onions and cumin over medium heat until soft, about 4 minutes. Add the tomatillos and cook until slightly browned, about 8 minutes. If needed, add a couple splashes of chicken broth and/or fat to keep everything moist.
Add the pork back into the pot along with half the pre-prepared green sauce, remaining chicken broth, diced chiles and oregano. Bring to a bubble and simmer uncovered on medium low until the pork is cooked through and tender, about 2 hours. Keep an eye on the pot, stir occasionally and add additional water or broth if the liquid level gets too low.
Add the sweet potato and remaining green sauce and continue to simmer until the potatoes are soft, about 30 minutes.