Pour the cream into a medium heavy-based pan, add the Parmesan rind and any bacon rind. Bring to a gentle bubble and allow to reduce for 5-6 minutes.
Place the pasta into a large pan of salted boiling water and cook for 4-5 minutes or until al dente.
Meanwhile heat a heavy-based wok or large frying pan. Add one tablespoon of the oil and then the bacon. Cook the bacon for 2-3 minutes until really crispy. Next add remaining oil and the mushrooms and cook for a further 2-3 minutes.
Drain the pasta, tip into the frying pan and toss really well. Pour the cream into the pan through a sieve and add the cooked chicken. Season thoroughly with salt and freshly ground black pepper, then toss thoroughly again.
Finally add the mixed leaves, give the dish one last toss and then serve immediately in warmed deep bowls, with the Parmesan sprinkled on top.