Trim the cavolo nero, removing the tough central stalks, then roughly shred.
Heat the oil in a large frying pan over a medium heat, add the garlic and chilli and cook, stirring, until the garlic just begins to colour. Toss in the cavolo nero and season with salt. Cook, stirring, over a high heat for 2–3 minutes until softened.
Cook the pasta in a large saucepan of salted boiling water according to the packet instructions until al dente. Drain, reserving a ladleful of the cooking water.
Meanwhile, pour the cream over the wilted cabbage and bring to the boil. Reduce the heat to a slow simmer and cook for 5 minutes until the cream has thickened so that it coats the cabbage in a silky sauce. Add the pecorino and pasta and stir over a low heat for 30 seconds. Pour in the reserved pasta cooking water and continue stirring until the pasta is well coated and looks silky. Serve immediately with a scattering of grated pecorino.