Place heavy cream and 2 cups of stock in a large heavy-bottomed pot and bring to a light boil.
Remove from heat and whisk in lemon juice and lemon zest.
Add pasta and cook on low heat until pasta begins to soften. Stir continuously so that pasta is evenly coated with the sauce (about 5 to 10 minutes, depending on how soft you like your pasta).
Remove from heat and stir in ½ cup parmesan cheese and cold butter.
Let sit for a few minutes before serving, this will allow the pasta sauce to thicken up and develop that creamy texture.
Season with salt and pepper and garnish with remaining parmesan cheese and parsley.