Preheat the slow cooker if necessary; see the manufacturer's instructions. Heat the butter and oil in a large frying pan, then add the white leek slices, the diced bacon and potatoes and fry over a medium heat, stirring, until just beginning to turn golden.
Pour in the stock, add a little salt and pepper and bring to the boil, stirring. Transfer to the slow cooker pot, cover with the lid and cook on low for 5–6 hours. Stir the reserved green leek slices and milk into the slow cooker pot. Replace the lid and cook, still on low, for 30 minutes or until the leeks are tender. Roughly purée the soup in the pot with a stick blender or use a masher, if preferred.
Mix in the cream and two-thirds of the cheese and continue stirring until the cheese has melted. Taste and adjust the seasoning, if needed, then ladle the soup into bowls and sprinkle with the remaining cheese and chopped grilled bacon.