Bring a large pot of heavily salted water to boil and cook pasta according to package directions. Be sure to reserve about 1 cup of cooking liquid when draining pasta.
Coat shrimp evenly in olive oil and liberally season with salt and pepper.
In a large skillet, heat a few tablespoons of olive oil over medium heat. Working in batches, sauté shrimp about 2-3 minutes per side, until pink and cooked through. Add additional olive oil between batches as needed.
When cooked, remove shrimp and set aside in a plate.
In the same skillet, reduce heat slightly and melt butter. Add garlic cloves and Italian seasoning. Sauté a minute or so until garlic is fragrant.
Add heavy cream, parmesan and cream cheese. Heat mixture through until sauce comes together and cheese is melted.
Add parsley and lemon zest. Stir to combine. Season sauce with salt and pepper as needed.
Add drained pasta and shrimp (along with juices from plate) to the sauce and thoroughly combine. Heat until shrimp is warmed. Add reserved pasta water to thin sauce to desired consistency as needed.
Garnish with more fresh parsley, lemon zest, parmesan cheese, and red pepper flakes if desired.