Bring a large pan of salted water to the boil and add the fusilli pasta. Bring back to the boil and then simmer according to the instructions on the packet (usually 8-12 minutes). When cooked it should still be slightly firm to the bite. Drain the pasta in a colander, reserving a ladleful of the pasta water.
While the pasta is cooking, heat the olive oil in a frying pan over a medium-high heat and cook the bacon pieces until slightly browned. Remove the bacon from the pan and set aside.
Add the cream and frozen peas to the frying pan and bring to the boil. Cook for a few minutes until the peas are defrosted and heated through and the cream sauce has thickened. Add the ladleful of pasta water, the pinch of salt and pepper and mix until combined.
Add the drained pasta to the sauce and mix together until everything is coated with the cream.
Serve immediately with a generous grating of parmesan cheese on top.