In a large skillet over medium heat, sauté onion and carrot in the oil until onion is softened; add chilies and garlic and continue to sauté for 2 to 3 minutes; transfer to a slow cooker.
Combine salt, pepper, oregano, cumin and coriander; rub into the surface of the pork roast. Place roast in slow cooker; pour chicken broth and water AROUND (not over) roast.
Cover and cook on low heat setting for 8 hours, or until pork is tender.