In a large pot, bring water to boil and cook spaghetti until al dente (about 7 minutes).
Drain pasta and set aside. Don't forget to reserve your pasta water.
In the same large pot over medium heat add olive oil, butter, garlic and red pepper flakes for about 3 minutes. This lets the garlic and red pepper really infuse into the oil.
Add lemon juice, pasta water, and cream and bring to a low boil for about 2 minutes,
Reduce heat to low and add ¾ cup of Parmigiano Reggiano and lemon zest to sauce.
Remove pot from heat and add spaghetti and let it absorb the sauce for a few minutes.
Garnish with basil, parsley, and remaining cheese.