Bring a large pot of well-salted water to a boil. Once boiling, cook pasta according to package instructions. Once pasta has cooked, reserve about 1 cup of pasta water before draining noodles. While pasta is cooking, begin preparing lemon sauce.
In a large saucepan, combine oil and butter over medium heat.
Once butter is melted, add shallot, lemon zest, and crushed red pepper and cook until shallot is translucent (if substituting garlic, cook just until garlic is fragrant/30 seconds).
Whisk in 2 Tablespoons of lemon juice until combined.
While whisking constantly, slowly drizzle in heavy cream and whisk until combined.
Bring mixture to a simmer (while stirring frequently). Once simmering, reduce heat to low and add parmesan cheese, salt, and pepper.
Add warm, cooked spaghetti to the pan along with a splash (2-3 Tablespoons) of pasta water. Toss together over low heat until pasta is well combined and well coated with the sauce.
Top with fresh parsley, if desired, and serve.
