Prepare the Chile Sauce: In a large pot, heat the vegetable oil over medium heat. Add the chopped onion and garlic, sauté until soft and fragrant. Stir in the red chile powder, then gradually add the chicken broth, stirring constantly to create a smooth sauce.
Season the Sauce: Add the oregano, cumin, salt, and black pepper to the sauce. Bring to a simmer and let it cook for about 10 minutes to allow the flavors to blend.
Marinate the Pork: Place the pork cubes in a large bowl. Pour the chile sauce over the pork, making sure it's well-coated. Cover and refrigerate for at least 4 hours, but preferably overnight.
Cook the Pork: Preheat your oven to 325°F (165°C). Transfer the pork and sauce to a baking dish, cover with foil, and bake for about 2 to 2.5 hours, or until the pork is tender and the sauce has thickened.
Finish and Serve: Stir in the apple cider vinegar before serving. Serve hot with rice, beans, tortillas, or as a filling for burritos.