Add a good splash of the olive oil to a frying pan. Set over a medium heat and fry the breadcrumbs until crisp and golden brown. Season with sea salt then drain and reserve.
Place a medium pan of salted water over a high heat and bring to the boil. Plunge in the cabbage and cook on a rolling boil for 5 minutes or so until tender. Immediately remove with a slotted spoon and transfer to a blender together with a ladleful of the cooking liquid.
Blend to a smooth puree then transfer to a large frying pan and reserve.
Cook the pasta in the remaining cabbage water until al dente then drain the pasta ( reserving the water) and transfer to the cabbage puree. Add a good lug of olive oil and half the pecorino.
Turn on the heat, add a ladleful of the cooking water and toss the pasta in the puree to coat. Divide between four bowls . Top with the remaining pecorino and the fried breadcrumbs and serve immediately.