Preheat the oven to 325 degrees F.
In a large oven-safe Dutch oven, melt the butter over medium-high heat. Sprinkle the salt and cumin over the pork. Working in batches, add the pork to the pan and brown on all sides, about 5 minutes per batch. Remove and set aside.
In the same pot, add the onions, poblano pepper, jalapeno and garlic, and cook until the onion softens, about 5 minutes. Stir in the chicken broth, salsa, hominy and pork. Cover and bake until the pork is tender, about 1 hour and 20 minutes. Skim any fat from the top. Stir in the cilantro and serve.