Heat the oil in a large pan over medium heat; add pork shoulder and brown on all sides. Reserve the juices in the pan and transfer the pork to a slow cooker.
In the pan with the pork juices, add the onion and garlic and cook for about 1 minute over low heat. Transfer all the contents of the pan into the slow cooker.
Mix the tomatillos, green chilli peppers, jalapeno peppers and coriander into the slow cooker. Season with oregano, salt and pepper. Add 1 litre of water, or enough to cover all ingredients. Cover and cook on High for 6 to 7 hours.
Shred the cooked pork with a fork. Spoon the slow cooker mixture into bowls and top with grated cheese, soured cream and fresh coriander sprigs to serve.