In a large pot, bring salted water to boil and cook pasta.
Drain and reserve one cup of the pasta water.In a food processor, add the basil leaves and a large pinch of kosher salt. Turn on the machine and pour in the cream. Continue processing until the mixture starts to turn green and thicken. Be careful not to over blend or the cream will break.
In a separate pan, heat the reserved pasta water and add the basil and cream mixture. Bring to a simmer and reduce slowly until sauce easily coats the back of a spoon.
Add the basil cream to the pasta and combine until nicely coated. Season with salt and pepper to taste.
Garnish with freshly grated parmesan cheese and serve hot.