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Chop the onion, carrot, celery and garlic in a food processor. Heat the oil over a medium heat in a large saucepan. Add the vegetables and potatoes, season well, then reduce the heat and cover the pan. Gently cook for about 5 mins until starting to soften, then add the stock, turn up the heat and bring to the boil. Simmer for 5 mins more, or until all the vegetables are tender.
While the soup is cooking, grill or fry the bacon until crisp, then cut into strips. Shred the cabbage, discarding the core.
Whizz the soup in the food processor until smooth, then return to the pan and add the cabbage. Simmer for a few mins until the cabbage is just tender, then season to taste and serve scattered with the bacon.