Bring a large pan of water to the boil and cook the pasta according to the pack instructions (usually 10-12 minutes).
Whilst the pasta is cooking, heat the oil in a frying pan until very hot, then cook the bacon until browned and crispy (about 5 minutes). Turn a couple of times during cooking. Remove from pan and chop into small pieces.
Keep the frying pan on the heat, but turn the heat down to low (there should still be some bacon fat in there). Place the kale in the bacon pan and let it cook in the hot oil for 1 minute. Turn off the heat.
When the pasta is cooked, drain it, reserving 1 cup of the cooking water.
Put the pasta back in the pan and place over a low heat. Stir in the cheese and cream, then once the cheese has melted, stir in the kale and bacon. Heat through for 1 minute. If the pasta looks a little dry, add in a good splash of the pasta cooking water.