Set a large pot of salted water to boil. Mince the garlic and zest the lemons.
Heat the butter over low heat. Add the garlic and cook gently. They shouldn't get brown, only softened.
Cook the pasta according the package instructions, but with two minutes less on the cook time. It'll finish cooking in the sauce.
When the garlic is softened and fragrant, add cream, olive oil, zest of three lemons and juice of only two. Cook on low heat for 3-5 minutes, until slightly reduced, stirring regularly.
When the pasta is done, set aside ½ cup pasta water then drain the spaghetti. Pour a few tablespoons of the pasta water into the sauce, then add spaghetti. Toss well to coat the pasta using tongs, adding more pasta water if you need it. Add a generous pinch of salt and pepper to taste.
Top with parsley and parmesan and serve immediately!