Bring a pot of water to a boil and begin to cook the pasta as per the directions on the box.
While the pasta cooks, add the cream to a large saucepan and bring to a simmer over a medium low heat.
Add the lemon zest, salt and pepper and bring to a simmer.
Once the cream begins to bubble add the Parmesan and mix until smooth.
Add the shrimp and cook until the shrimp are cooked through, about 3-4 minutes.
Using a set of tongs, grab some of the pasta from the pot and add it to the cream sauce.
Mix well making sure the pasta is well coated in sauce. Add more pasta if you think there is enough sauce to coat it.
Transfer the pasta with shrimp to a plate and garnish with some extra Parmesan and chopped basil.
Serve at once.