Chop the bacon and fry it till done but not crispy.
Meanwhile, chop the chestnuts.
Drain any excess fat off the bacon, and stir in the chestnuts. Stir in the greens, cook for about 5 minutes till the greens are all wilted. Mix the mustard into the cream, then stir this into the greens. Heat through, adjust taste with salt and pepper, serve hot.
If your bacon doesn't have any fat on it, use the oil to fry it in; if your bacon is a streaky bacon or American bacon, you won't need the oil. You can use tinned chestnuts; drain them first.