Wash chilies; remove stems and seeds. Place in 3-qt. pan with water.Cover and simmer 20 minutes, or until chilies are very soft. Pour chilies and liquid into blender; puree. Push puree through wire strainer; discard pulp. Add onion, garlic, oregano, salt and cumin to chili mixture.
If using pork butt, trim excess fat. Cut meat into 1/2 inch slices, then cut into strips about 1 inch wide and 3 inches long. If using pork chops, trim fat.
Place meat in heavy self-sealing plastic bag. Pour chili mixture over meat; seal bag. Refrigerate 1 to 2 days.
Preheat oven to 325*. Transfer meat and chili mixture to 2 1/2 quart casserole dish; cover. Bake 2 to 2 1/2 hours or until meat is very tender. Skim and discard fat before serving.