Cook pasta according to package directions. Drain and then stir in 1 oz oil to coat pasta.
While pasta is cooking, melt butter in a medium sauce pan over low heat, then add heavy cream. Increase heat to medium-high stirring occasionally and when the mixture begins to bubble, add in the Parmesan cheese and blend until the cheese has melted. Add in lemon juice and lemon zest and stir. Season with black pepper and salt to taste.
Add cooked pasta and mix well. Bring sauce back to just under a boil and then serve. You may wish to garnish your pasta dish with some additional Parmesan cheese, parsley, or even a couple of capers. This dish does not re-heat well, so plan on enjoying this dish in one setting.